Practice Test

Q1) If the point (0, 0), (1, 0), (0, 1) and (t, t) are con-cyclic, then t is equal to Show Answer

Q2) The equation of the circle which touches the axis of y at the origin and passes through (3, 4) is Show Answer

Q3) The center of the circle passing through (0, 0), (a, 0) and (0, b) is Show Answer

Q4) The area of the circle having (1, 2) as center and passing through
(4, 6) is Show Answer

Q5) Equation of the circle passing through (4, 5) having center at (2, 2) is Show Answer

Q6) The circle described on the line joining the point (0, 1), (a, b) as diameter cuts the x-axis in points whose abscissae are the roots of the equation Show Answer

Q7) Equation of the circle which passes through
(3, 6) and touches the axes is Show Answer

Q8) Equation of the circle with center on the y-axis and passing through the origin and (2, 3) is Show Answer

Q9) The lines 3 x - 4 y + 4 = 0 and 6 x - 8 y - 7 = 0 are tangents to the same circle, then its radius is Show Answer

Q10) The equation of the circle passing through (4, 5) having center at (2, 2) is Show Answer

Q11) The line 2 x - 3 y = 5 and 3 x - 4 y = 7 are diameters of a circle of area 154 sq. units; then the equation of this circle is Show Answer

Q12) Locus of a point which moves such that the sum of the squares of its diameters from the sides of a square of side unity is 9, is Show Answer

Q13) The lines 3 x - 4 y + 4 = 0 and 3 x - 4 y - 5 = 0 are tangents to the same circle. The radius of this circle is Show Answer

Q14) Center of the circle is
(2, 3). If the line x + y = 1 touches it, its equation is Show Answer

Q15) If (x, 3) and (3, 5) are the extremities of a diameter of a circle with center at (2, y), then the values of x and y are Show Answer

Q16) Locus of the center of the circle which always passes through the fixed points (a, 0) and (-a, 0) is Show Answer

Q17) The points (2, 3), (0, 2), (4, 5), (0, C) are concyclic if the value of C is Show Answer

Q18) The equation to a circle whose center lies at the point (-2, 1) and which touches the line 3 x - 2 y - 6 = 0 at (4, 3) is Show Answer

Q19) The radius of the circle passing through the point P (6, 2), two of whose diameters are x + y = 6 and x + 2 y = 4 is Show Answer

Q20) The equation of a circle with origin as center and passing through the vertices of an equilateral triangle whose median is of length 3a is Show Answer

Q21) Equation of the circle having diameters 2 x - 3 y = 5 and 3 x - 3 y = 7 and radius 8 is Show Answer

Q22) A circle has radius 3 units and its center lies on y = x - 1. If it passes through the point (7, 3); its equation is Show Answer

Q23) The line 3 x - 4 y + 4 = 0 and 6 x - 8 y - 7 = 0 are tangents to the same circle; then the radius of the circle is Show Answer

Q24) The equation of the circle which has a tangent 2 x - y - 1 = 0 at (3, 5) on it and with the center on (x + y) = 5 is Show Answer

Q25) Equation of the circle through the origin which cuts intercepts of length a and b on axes is Show Answer

Q26) The equation of the circle passing through (2, 1) and touching coordinate axes is Show Answer

Q27) If (p, q) is the center of a circle passing through the origin, then the equation of this circle is Show Answer

Q28) The equation of the circle passing through (4, 5) having the center at (2, 2) is Show Answer

Q29) Equation of circle which passes through the points (1, -2) and (3, -4) and touch the x-axis is Show Answer

Q30) The area of circle centered at (1, 2) and passing through (4, 6) is Show Answer

Q31) The lines 2 x - 3 y = 5 and 3 x - 4 y = 7 are diameters of a circle of area 154 sq units. Then, the equation of this circle is Show Answer

Q32) The radius of the circle passing through the point P (6, 2), two of whose diameter are x + y = 6 and x + 2 y = 4 is Show Answer

Q33) If (x, 3) and (3, 5) are the extremities of a diameter of a circle with center at (2, y), then the values of x and y are Show Answer

Q34) Locus of the center of the circle which always passes through the fixed points (a, 0) and (-a, 0) is Show Answer

Q35) Which of the following is true? Show Answer

Q36) If given points are the ends of diameter, then the equation of circle is Show Answer

Q37) How many tangents can be drawn from the origin to the circle that we get in above question? Show Answer

Q38) Which one of the following points lies inside a circle of radius 6 and center at (3, 5)? Show Answer

Q39) The angle subtended at the center of a circle of radius 3 cm by an arc of length 1 cm is Show Answer

Q40) The radius of a circle is uniformly increasing at the rate of 3 cm/s. What is the rate of increase in area, when the radius is 10 cm? Show Answer

Q41) What is the radius of the circle touching X-axis at (3, 0) and Y-axis at (0, 3)? Show Answer

Q42) What is the equation to circle which touches both the axes and has center on the line x + y = 4? Show Answer