Practice Test

Q1) The line segments passing through the points (-2,-1) and (2,1) subtend right angle at P, the locus of P is _____. Show Answer

Q2) The co-ordinates of the orthocenter of the triangle formed by (0,0),(8,0),(4,6) is _____. Show Answer

Q3) The equation of the line through (1, 2), which makes equal intercepts on the axes, is _____. Show Answer

Q4) The equations of the locus of point P which is equidistant from the points (-5, 4) and (3, -2) is Show Answer

Q5) A(-3, 0) and B(3, 0) are the two given points. Find the equation of the locus of points such that PA + PB = 10? Show Answer

Q6) If the origin is shifted to the point (-5, -2) the axes remaining parallel, then the new coordinates of the point (4, 6) is Show Answer

Q7) If the origin is shifted to the point (7, -2) the axes remaining parallel, then the old coordinates of the point (-4, -1) and (-2, 3) are Show Answer

Q8) If the origin is shifted to (3, -1), axes remaining parallel, (3, b) lies on the new X-axis and (a,-1) lies on the new Y-axis, then the values of a and b are Show Answer

Q9) On shifting the origin to (h, k) axes remaining parallel the co-ordinates of (5, 4) become (-3, -1). Then h &k are Show Answer

Q10) The equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from axes, is Show Answer

Q11) The equation of the straight line which passes through the point (3, 2) and perpendicular to the line y = x is Show Answer

Q12) If the midpoints of the sides BC, CA and AB of the triangle ABC are (1, 3), (5, 7) and (-5, 7), then the equations of the side AB is Show Answer

Q13) If the co-ordinates of the vertices A, B and C of the triangle ABC be (-1, 6), (-3, -9), (5, -8) respectively, then the equations of the median through C is Show Answer

Q14) The equation of the line joining the origin to the point (-4, 5), is Show Answer

Q15) The equation of the line which cuts off an intercept 3 units on OX and an intercept -2 units on OY, is Show Answer

Q16) The equations of a line through the intersection of lines x = 0 and y = 0 and through the point (2, 2) is Show Answer

Q17) The equation of line, which bisect the line joining two points (2, -19) and (6, 1) and perpendicular to the line joining two points (-1, 3) and (5, -1), is Show Answer

Q18) The line joining the points (-1, 3) and (4, -2) passes through the point (p, q) if Show Answer

Q19) If (2,-6) and (-3,-5) lie on the locus ax + by =1, then a and b are Show Answer

Q20) The line segment joining (2,-1) and (-2,1) subtends a right angle at P. The locus of P is Show Answer

Q21) Equation of the locus of the point P, such that the ordinate of P exceeds three times its abscissa by 1, is Show Answer

Q22) If origin is shifted to the point (-2,4), axes remaining parallel, (4,b) lies on the new X-axes and (a,-5) lies on the new Y-axes, then values of a and b are Show Answer

Q23) If A is (5,-3) and B is a point on the X-axis such that the slope of line AB is -2, then B = ... Show Answer

Q24) If the line kx+4y=6 passes through the point of intersection of the two lines 2x+3y=4 and 3x+4y=5 then k = Show Answer

Q25) A line passes through (2,2) and is perpendicular to the line 3x+y=3. Its y-intercept is Show Answer

Q26) A line through the point A (3,4) is such that its intercepts between the axes is bisected at A. Its equation is Show Answer

Q27) The inclination of the line passing through the point (5,6) and the midpoint of the line joining the points (4,-5) and (-2,9) is Show Answer

Q28) The orthocentre of the triangle whose vertices are (0,0), (3,0), (0,4) is Show Answer

Q29) A(-1,1), B(5,3) are opposite vertices of a square in the XY-plane. The equation of the other diagonal (not passing through A,B) of the square is given by Show Answer

Q30) The points (3,3), (h,0) and (0,k) are collinear, if Show Answer

Q31) If each of the points (a,4) and (-2,b) lies on the line joining the points (2,-1), (5,-3) then the point P (a,b) lies on the line Show Answer

Q32) The distance between the parallel lines y = 2x+4 and 3y=6x-5 is equal to Show Answer

Q33) The equation of the locus of P such that abscissa of P exceeds twice its ordinate by 1 is y = 2x +1. Show Answer

Q34) The equation of the locus of P such that ordinate of P exceeds its abscissa by 2 is y=x+2. Show Answer

Q35) The locus of the point whose distance from X-axis is twice that from Y-axis is y=2x. Show Answer

Q36) If the origin is shifted to O' (1,2) axes remaining parallel, then the new distance between A=(5,7) and B=(2,3) changes. Show Answer

Q37) A line parallel to Y-axis has no y-intercept. Show Answer

Q38) If a line is passing through the origin, then its both x-and y-intercepts are zero. Show Answer

Q39) If the slopes of two lines do not exist, then they are perpendicular to each other. Show Answer

Q40) The equation of the line containing the point A(2,3) and perpendicular to X-axis is x=2. Show Answer

Q41) The slope of the line which makes equal intercepts of opposite signs on the coordinate axes is -1. Show Answer

Q42) The line joining the points (3,-4) and (-2,6) is perpendicular to the line joining the points (-3,6) and (9,18). Show Answer

Q43) The points A (-2,1), B(0,5) C(-1,2) are collinear. Show Answer

Q44) The straight line 5x+4y=0 passes through the point of intersection of the straight lines x+2y-10=0 and 2x+y+5=0. Show Answer

Q45) The equation of the line having slope 5 and making intercept on the X- axis is y=5x+5. Show Answer

Q46) The coordinates of point on the Y-axis such that the slope of the line containing that point and the point (-4,9) is -1, are (0,5). Show Answer

Q47) The equation of line passing through the origin and the middle point of the intercept of the line ax + by + c = 0 between the axes, is ax + by =0. Show Answer

Q48) If a line ax + by + c =0 is parallel to X-axis, then a=0. Show Answer

Q49) If a line ax + by + c =0 is perpendicular to X-axis, then a=0. Show Answer

Q50) N (3,-4) is the foot of perpendicular drawn from the origin to the line L. Then the equation of the line L is 3x-4y=25. Show Answer

Q51) If the length of perpendicular from the point (4,1) on the line 3x-4y+k=0 is 2 units, then the value of k is -2 or 18. Show Answer