Practice Test

Q1) A normal to any circle always lies along its Show Answer

Q2) If lines 12x + 5y + 16 = 0 and 12x + 5y - 10 = 0 both touch the same circle, then radius of this circle is Show Answer

Q3) If equation of common tangent at (1, -1) to two circles, each of radius 13, is 12x + 5y - 7 = 0, then centres of circles are Show Answer

Q4) Line 3x + y = 0 touches a circle centered at (2,-1). Then, other tangent to this circle from the origin is Show Answer

Q5) If two circles of same radius r and centres at (2, 3) and (5, 6) cut each other orthogonally, then r = Show Answer

Q6) Radius of the larger circle in the first quadrant which touches the line 4x + 3y - 12 = 0, and the co-ordinate axes, is Show Answer

Q7) Centre of the circle lies on the line x + 2y = 3 as well as on the bisector of the angle in the first quadrant. If this circle touches the line 4x + 8y = 7, then its area is Show Answer

Q8) A circle touches both the axes, and the line 4x + 3y = 6 in the first quadrant. If it lies entirely below the line, then its equation is Show Answer

Q9) The equation of the circle having x - y - 2 = 0 and x - y + 2 = 0 as two tangents, and x - y = 0 as a diameter, is Show Answer

Q10) If two circles cut each other orthogonally, then Show Answer

Q11) A circle passes through the origin (2, 0) and (0, 4). Co-ordinates of its center are Show Answer

Q12) Equation of the circle passing through the origin, and the points of intersection of the line 4x + 3y = 12 with the co-ordinate axes, is Show Answer

Q13) If 2x + 3y = 7 and x - 3y = -10 are two diameters of a circle passing through (11, -2), then the length of its diameter is Show Answer

Q14) Equation of the circle having 12x + 5y + 7 = 0 as a tangent, and x + y = 1, x - y = 3 as two normals, is Show Answer

Q15) Equation of the circum - circle of the tangent formed by the lines x = 0, y = 0 and 3x - 4y = 12 is Show Answer

Q16) If y = 2x is a tangent to a circle centred at (1,1), then the other tangent from the origin to this circle is Show Answer

Q17) If a circle whose centre is at (1,2) touches the line x+ 3y = 3, then their point of contact is Show Answer

Q18) Tangents at the ends of a focal chord of a parabola meet each other Show Answer

Q19) The only real normal to a parabola, passing through its focus, is its Show Answer

Q20) Point of intersection of two perpendicular tangents to a parabola lies on the Show Answer

Q21) Equation of the parabola with vertex at the origin, Y-axis as the axis and passing through (3, 9) is Show Answer

Q22) Two lines x - 2y = 4 and 7x + 2y + 20 = 0 touch an ellipse whose equation is Show Answer

Q23) If the line 3x + 2y = 8 touches the ellipse whose semi-minor axis is 2, then the equation of this ellipse is Show Answer

Q24) If the product of lengths of perpendiculars drawn from the foci of a hyperbola to its tangent 2x - y + 4 = 0 is 9, then the equation of this hyperbola is Show Answer

Q25) If conjugate axis equals latus-rectum, then: e = Show Answer

Q26) Find the equation of the circle which touches the both axes in first quadrant and whose radius is a. Show Answer

Q27) Equation of a circle which passes through (3,6) and touches the axes is Show Answer

Q28) Equation of the circle with centre on the y-axis and passing through the origin and the point (2,3) is Show Answer

Q29) If the lines 2x - 3y = 5 and 3x - 4y = 7 are the diameters of a circle of area 154 sq units, then find the equation of the circle. Show Answer

Q30) Find the equation of the circle which passes through the points (2,3) and (4,5) and the centre lies on the straight line y - 4x + 3 = 0. Show Answer

Q31) The normal at the point (3,4) on a circle cuts the circle at the point (-1, -2). Then, the equation of the circle is Show Answer

Q32) If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then find the radius of the circle. Show Answer

Q33) Find the equation of a circle which touches both the axes and the line 3x - 4y + 8 = 0 and lies in the third quadrant. Show Answer

Q34) Two circles with centres (2,3) and (5,6) cut orthogonally. If radius of both circles are equal, then radius is equal to Show Answer

Q35) If two circles, each of radius 5 units, touch each other at (1,2) and the equation of their common tangent is 4x + 3y = 10, then equation of the circle a portion of which lies in all the quadrants, is Show Answer

Q36) The area of the circle centred at (1,2) and passing through (4,6) is Show Answer

Q37) If a circle passes through the point (0, 0), ( a, 0) and (0, b), then find the coordinates of its centre. Show Answer

Q38) The distinct points A ( 0,0 ), B ( 0,1 ), C ( 1,0 ) and D ( 2a, 3a) are concyclic, then Show Answer

Q39) The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is Show Answer

Q40) Let PQ and PS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point x on the circumference of the circle, then 2r equals Show Answer

Q41) Two rods of lengths a and b slide along the x-axis and y-axis respectively in such a manner that their ends are concyclic. The locus of the centre of the circle passing through the end points is Show Answer

Q42) Statement I: Number of circles passing through (-2, 1), (-1, 0), (-4, 3) is 1.
Statement II: Through three non-collinear points in a plane only one circle can be drawn. Show Answer

Q43) The circle passing through (1, -2) and touching the axis to x at (3,0) also passes through the point Show Answer

Q44) The length of the diameter of the circle which touches the x-axis at the point (1,0) and passes through the point (2,3) is Show Answer

Q45) The equation of the circle passing through the points (1,0) and (0,1) and having the smallest radius is Show Answer

Q46) Consider a family of circles which are passing through the point (-1,1) and are tangent to x-axis. If (h,k) is the centre of circle, then Show Answer

Q47) A circle touches the x-axis and also touches the circle with centre at ( 0,3) and radius 2. The locus of the centre of the circle is Show Answer

Q48) The smallest circle with centre on y- axis and passing through the point (7,3) has radius Show Answer

Q49) A variable circle passes through the first point A ( p,q) and touches x-axis. The locus of the other end of the diameter through A is Show Answer

Q50) The equation of latusrectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y =12, then length of the latusrectum is Show Answer

Q51) If the focus of a parabola is ( 0, -3 ) and its directrix is y = 3 and its equation is Show Answer

Q52) If the vertex of the parabola is the point ( -3, 0 ) and the directrix is the line x + 5 = 0, then its equation is Show Answer

Q53) If the point ( 0, 4 ) and (0, 2) are respectively the vertex and focus of a parabola, then the equation of the parabola is Show Answer

Q54) The equation of parabola having vertex ( 0, 0 ) passing through ( 2, 3 ) and axis is along x-axis is Show Answer

Q55) Tangent at the vertex divides the distance between directrix and latusrectum in the ratio Show Answer

Q56) If the tangles at P and Q on the parabola meet in T, then SP, ST and SQ are in Show Answer

Q57) If the tangent and normal at any point P of a parabola meet the axes in T and G respectively, then Show Answer

Q58) If a parabola reflector is 20 cm in diameter and 5 cm deep, then the focus is Show Answer

Q59) The equation of the parabola whose focus is the point ( 0, 0 ) and the tangent at the vertex is x - y + 1 = 0, is Show Answer

Q60) The equation of the parabola whose focus is the point ( 0, 0 ) and the tangent at the vertex is x - y + 1 = 0 is Show Answer

Q61) The radius of circle when a attains its maximum value Show Answer

Q62) The slope of the tangent when radius of the circle is maximum is Show Answer

Q63) The minimum area bounded by the tangent and the coordinate axes is Show Answer

Q64) A parabola has the origin as its focus and the line x = 2 as the directrix. Then, the vertex of the parabola is at Show Answer

Q65) The locus of a point which moves such that the sum of its distances from two fixed points is always a constant, is Show Answer

Q66) Find the equation of an ellipse, if major axis on the x-axis and passes through the points ( 4, 3 ) and ( 6, 2 ). Show Answer

Q67) The sum of focal distance of any point on the ellipse with major and minor axes as 2 a and 2 b respectively, is equal to Show Answer

Q68) A man running round a race course notes that the sum of the distance of two flag posts from him is always 10 m and the distance between the flag posts is 8 m. The area of the path he encloses ( in square meter ) is Show Answer

Q69) If a bar of given length moves with its extremities on two fixed straight lines at right angles, then the locus of any point on bar marked on the bar describes a / an Show Answer

Q70) The eccentricity of the ellipse is Show Answer

Q71) Equation of auxiliary circle of ellipse is Show Answer

Q72) Length of latusrectum of the ellipse is Show Answer

Q73) In an ellipse, the distance between its foci is 6 and minor axis is 8. Then, its eccentricity is Show Answer

Q74) The eccentricity of an ellipse, with centre at the origin, is 1 / 2. if one directrix as x = 4, the equation of the ellipse is Show Answer

Q75) A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2, then length of semi-major axis is Show Answer

Q76) The eccentricity of the hyperbola whose latusrectum is 8 and conjugate axis is equal to half of the distance between the foci is Show Answer

Q77) The equation of the hyperbola whose foci are ( 6, 4 ) and ( - 4, 4 ) and eccentricity 2, is Show Answer

Q78) The asymptotes of the hyperbola xy = hx + ky are Show Answer

Q79) Eccentricity of hyperbola whose asymptotes are 3x - 4y = 7 and 4x + 3y = 8, is Show Answer

Q80) A hyperbola has the asymptotes x + 2y = 3 and x - y = 0 and passes through ( 2, 1 ). Its centre is Show Answer

Q81) The length of the transverse axis of the rectangular hyperbola xy = 18 is Show Answer

Q82) The normal at P to a hyperbola of eccentricity e, intersects its transverse and conjugate axes at L and M respectively. If locus of the mid-point of L M is hyperbola, then eccentricity of the hyperbola is Show Answer

Q83) If L is the chord of contact of the hyperbola H, then the equation of the corresponding pair of tangles is Show Answer

Q84) If R is the point of intersection of the tangles of H at the extremities of the chord L, then equation of the chord of contact of R with respect to the parabola P is Show Answer

Q85) STATEMENT I Asymptotes of hyperbola 3x + 4y = 2 and 4x - 3y = 5 are bisectors of transverse and conjugate axes of hyperbola.
STATEMENT II transverse and conjugate axes of hyperbola of the asymptotes. Show Answer

Q86) If the focus of a parabola divides a focal chord of
the parabola in segments of length 3 and 2, the
length of the latus–rectum of the parabola is: Show Answer

Q87) The locus of a point, which moves, such that the
sum of the squares of its distances from three
vertices of a triangle is constant is : Show Answer

Q88) A circle of radius 5 units touches both the axes
and lies in the first quadrant. If the circle makes
one complete roll on x–axis along the positive
direction of x–axis, then its equation in new
position is : Show Answer

Q89) A man running round a race course notes that the sum of the distances of two flag posts from him is always 10 metres and the distance between the flag posts is 8 metres. The area of the path he encloses in square metres is: Show Answer

Q90) If the focal distance of an end of the minor axis of any ellipse (referred to its axes as the axis of x and y respectively) is k and the distance between the foci is 2h, then its equation is: Show Answer

Q91) In a model, it is shown that an arc of a bridge is semi-elliptical having major axis horizontal. If the length of the base is 9 m and the highest point of the bridge is 3 m from the horizontal; the best approximation of the height of the arch, 2 m from the centre of the base is: Show Answer

Q92) Chords of an ellipse are drawn through the positive end of the minor axis. Then their middle point lies on: Show Answer

Q93) An ellipse has OB as semi–minor axis, F and F' its foci and the angle FBF' is a right angle. Then the eccentricity of the ellipse is: Show Answer

Q94) Locus of the centre of a circle which touches given circle externally is: Show Answer

Q95) PM is perpendicular from a point on a rectangular hyperbola to its asymptotes, then the locus of the mid–point of PM is: Show Answer

Q96) A circle touches the x–axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is: Show Answer

Q97) Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2 CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD
touching all the sides, then its radius is : Show Answer

Q98) The circle passing through (1, –2) and touching
the axis of x at (3,0) also passesthrough the point: Show Answer

Q99) The equation of the circle passing through the
points (1,0) and (0, 1) and having smallest radius
is : Show Answer

Q100) Two vertices of an equilateral triangle are (-1,0) and (1,0) and its third vertex lies above the x-axis. The equation of its circumcircle, is Show Answer

Q101) In an ellipse the distance between the foci is 8 and the distance between the directrices is 25. The length of major axis is Show Answer

Q102) If the latusrectum of a hyperbola forms an equilateral triangle with the vertex at the center of the hyperbola, then the eccentricity of the hyperbola is Show Answer

Q103) The locus of a point which moves such that the difference of its distances from two fixed points is always a constant, is Show Answer

Q104) The normal at P to a hyperbola of eccentricity e, intersects its transverse and conjugate axes at L and M respectively. If locus of the mid point of LM is hyperbola, then eccentricity of the hyperbola is Show Answer

Q105) An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the necessary length of the string and the distance between the pins respectively in cms. are Show Answer

Q106) ABCD is a square whose side is a. The equation of the circle circumscribing the square, taking AB and AD as axes of reference, is Show Answer

Q107) Circles are drawn through the point (2,0) to cut intercepts of length 5 units on the x-axis. If their centres lie in the first quadrant, then their equation is Show Answer

Q108) If the vertex and focus of a parabola are (3,3) and (-3,3) respectively, then its equation is Show Answer

Q109) If the length of the major axis of an ellipse is three times the length of its minor axis, its eccentricity, is Show Answer

Q110) A straight rod of length 9 units with its ends A,B always on x and y axes respectively. then, the locus of the centroid of ∆ OAB, is Show Answer

Q111) S and T are the foci of an ellipse and B is end point of the minor axis . If STB is an equilateral triangle, the eccentricity of the ellipse is Show Answer

Q112) The eccentricity of the hyperbola can never be equal to Show Answer

Q113) The equation of the circle passing through (4, 5) and having the center (2, 2), is Show Answer

Q114) The equation of the parabola whose vertex is at (2,-1) and focus at (2,-3) is Show Answer

Q115) The line segment joining the points (4, 7) and (-2,-1) is a dismeter of a circle. If the circle intersects the x-axis at A and B, then AB is equal to Show Answer

Q116) ABCDIs a square whose side isa. If AB and AD are axes of coordinates, the equation of the circle circumscribing the square will be Show Answer

Q117) If (-4,3) and (8,3) are the vertices of an ellipse whose eccentricity is 5/6 then the equation of the ellipse is Show Answer

Q118) If the coordinates of the center, a focus and adjacent vertex are (2,-3),(3,-3) and (4,-3) respectively, then the equation of the ellipse is Show Answer

Q119) If the vertices of an ellipse are (-12,4) and (14,4) and eccentricity 12/13, then the equation of the ellipse is Show Answer

Q120) The equation of the mirror that can reflect all incident rays from origin parallel to y-axis is Show Answer

Q121) If the tangent and normal at any point P of a parabola meet the axes in Tand G respectively, then Show Answer

Q122) Equation of the circle through the origin and making intercepts of 3 and 4 on the positive sides of the axes is Show Answer

Q123) The parametric representation of a point of the ellipse whose foci are (3, 0) and (-1,0) and eccentricity 2/3 is Show Answer

Q124) Which of the following equations gives circle? Show Answer

Q125) If the vertex of a parabola is (0,2) and the extremities of latusrectum are (-6,4) and (6,4), then, its equation is Show Answer

Q126) If the focus and vertex of a parabola are the points (0,2) and (0,4) respectively, then its equation is Show Answer

Q127) In the standard form of an ellipse sum of the focal distances of a point is Show Answer

Q128) The equation of the hyperbola whose foci are (6,5),(-4,5) and eccentricity 5/4, is Show Answer

Q129) The difference of the focal distances of any point on the hyperbola is equal to its Show Answer

Q130) Equation of a common tangent with positive slope to the circle as well as to the hyperbola is Show Answer

Q131) All ellipse has its center at (1,-1) and semi-major axis = 8 and it passes through the point (1,3). The equation of the ellipse is Show Answer

Q132) The area of the circle whose center is at (2, 3) and passing through (4, 6), is Show Answer

Q133) If distance between directrices of a rectangular hyperbola is 10, then distance between its foci will be Show Answer

Q134) The equation of the parabola with vertex (-1,1) and focus (2,1) is Show Answer

Q135) Equation of the ellipse whose foci are (2,2) and (4,2) and the major axis is of length 10 is Show Answer

Q136) The eccentricity of a rectangular hyperbola is Show Answer

Q137) The locus of the poles of the focal chords of a parabola is …. of the parabola Show Answer

Q138) Suppose a circle passes through (2, 2) and (9, 9) and touches the x-axis atP. If O is the origin, then OP is equal to Show Answer

Q139) The two ends of latusrectum of a parabola are the points (3,6) and (-5,6). The focus is Show Answer

Q140) A variable circle passes through the fixed point (2,0) and touches y-axis. Then, the locus of its center is Show Answer

Q141) Equation of the parabola with its vertex at (1,1) and focus (3,1) is Show Answer

Q142) A line is at a constant distance c from the origin and meets the coordinate axes in A and B. The locus of the centre of the circle passing through O,A,B is Show Answer

Q143) For an ellipse with eccentricity 1/2 the centre is at the origin. If one directrix is x = 4, then the equation of the ellipse is Show Answer

Q144) If (0,6)and (0,3) are respectively the vertex and focus of a parabola, then its equation is Show Answer

Q145) A man running round a race course notes that the sum of the distances of two flag posts from him is always 10m and the distance between the flag posts is 8m. The area of the path he encloses (in square meter) is Show Answer

Q146) The points (5,-7) lies outside the circle Show Answer

Q147) If A,A' are the vertices, S,S' are the foci and Z,Z' are the feet of the directrices of an ellipse with centre C, then CS,CA,CZ are in Show Answer

Q148) The length of the latusrectum of an ellipse is one third of its major axis. Its eccentricity would be Show Answer

Q149) A circle touches y-axis at (0,2) and has an intercept of 4 units on the positive side of x-axis. The equation of the circle is Show Answer

Q150) The equation of the hyperbola of given transverse axis 2a with its vertex mid-way between the centre and the corresponding focus is Show Answer

Q151) The equation of the ellipse whose one focus is at (4,0) and whose eccentricity is 4/5 is Show Answer

Q152) The radical axis of the coaxial system of circles with limiting points (1, 2) and (-2,1)is Show Answer

Q153) The equation to the hyperbola having its eccentricity 2 and the distance between its foci is 8, is Show Answer

Q154) The equation of circle which touches the x-axis and y-axis at the points (1, 0) and (0, 1) respectively, is Show Answer

Q155) Coordinates of foci of hyperbola are (-5,3) and (7, 3) and eccentricity is 3/2. Then ,length of its latusrectum is Show Answer

Q156) The one which does not represent a hyperbola is Show Answer

Q157) A circle passes through (0,0),(a,0) and (0,b) the coordinates of its centre are Show Answer

Q158) If in a hyperbola, the distance between the foci is 10 and the transverse axis has length 8, then the length of its latusrectum is Show Answer

Q159) Extremities of a diagonal of a rectangle are (0 ,0) and (4 ,3). The equations of the tangents to the circumcircle of the rectangle which are parallel to the diagonal are Show Answer

Q160) If one end of the diameter is (1, 1) and the other end lies on the line x + y = 3, then locus of centre of circle is Show Answer

Q161) The equation of the smallest circle passing through the points (2, 2) and (3, 3) is Show Answer

Q162) The equation of the circle of radius 5 and touching the coordinate axes in third quadrant is Show Answer

Q163) The center of the circle passing through (0 ,0) (a ,0) and (0 ,b) is Show Answer

Q164) The equation of the parabola with its vertex at the origin, axis on the y-axis and passing through the point (6,-3) is Show Answer

Q165) The sum of focal distance of any point on the ellipse with major and minor axes as 2a and 2b respectively, is equal to Show Answer

Q166) The length of major and minor axis of an ellipse are 10 and 8 respectively and its major axis along y-axis the equation of the ellipse referred to its center as origin is Show Answer

Q167) The equation of two circles which touch the y-axis at (0, 3) and make an intercept of 8 unit on x-axis, are Show Answer

Q168) If the points (2, 0), (0, 1), (4, 5) and (0,c) are concyclic, then the value of c is Show Answer

Q169) The equation of the circle passing through (0,0) and belonging to the system of circles of which (3, 1) and (-1, 5) are limiting points, is Show Answer

Q170) The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the x and y-axes respectively are Show Answer

Q171) The parametric representation of a point on the ellipse whose foci are (-1,0) and (7,0) and eccentricity 1/2 is Show Answer

Q172) Four distinct points (2k, 3k),(1 ,0),(0 ,1) and (0,0) lie on a circle for Show Answer

Q173) The equation of family of circles with center at (h,k) touching the x-axis is given by Show Answer

Q174) The circle on focal radii of a parabola as diameter touches the Show Answer

Q175) A set of points is such that each point is three times as far away from the y-axis as it is from the point (4,0). Then, the locus of the points is Show Answer

Q176) If transverse and conjugate axes of hyperbola are equal then it’s eccentricity is Show Answer

Q177) Distance between foci is 8 and distance between directrices is 6 of hyperbola, then length of latus rectum is Show Answer

Q178) The number of maximum normals which can be drawn from a point to ellipse is Show Answer

Q179) he product of perpendiculars drawn from any point of a hyperbola to its asymptotes is Show Answer

Q180) The equation of the ellipse whose distance between foci is equal to 8 and distance between the directrix is 18, is Show Answer

Q181) AB is a diameter of a circle and C is any point on the circumference of the circle. Then, Show Answer

Q182) The area of the circle centered at (1, 2) and passing through (4, 6), is Show Answer