# Practice Test

Q1) Joint equation of co-ordinate axes, in a plane, is Show Answer

Q2) Joint equation of two lines both parallel to X-axis, and each at a distance of 2 units from it, is Show Answer

Q3) Joint equation of two lines both parallel to Y-axis, and each at a distance of 3 units from it, is Show Answer

Q4) Joint equation of two lines, through the origin, having slopes 2 and -2 is Show Answer

Q5) Joint equation of lines bisecting angles between co-ordinate axes is Show Answer

Q6) Joint equation of lines, trisecting angles in first and third quadrants, is Show Answer

Q7) Joint equation of lines, trisecting angles in second and fourth quadrants, is Show Answer

Q8) Combined equation of pair of lines, through (1, 2), and parallel to co-ordinate axes, is Show Answer

Q9) Joint equation of lines, through the origin, making an equilateral triangle with line x = 1, is Show Answer

Q10) Joint equation of lines, through the origin, making an equilateral triangle with line y = 2, is Show Answer

Q11) Joint equation of two lines through (-2, 3), parallel to bisectors of angles between co-ordinate axes, is Show Answer

Q12) Joint equation of the X-axis and the bisector of the angle in the first quadrant is Show Answer

Q13) For specifying a straight line, how many geometerical parameters should be known ? Show Answer

Q14) Slope of a line which cuts a intercepts of equal lengths on the axes is Show Answer

Q15) If the intercept of a line between the coordinate axes is divided by the point (-5, 4) in the ratio 1 : 2, then find the equation of the line. Show Answer

Q16) The straight line whose sum of the intercepts on the axes is equal to half of the product of the intercepts, passes through the point whose coordinates are Show Answer

Q17) If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3,2), then the equation of the line will be Show Answer

Q18) If the straight line ax + by + c = 0 always passes through (1, -2), then a, b, c are in Show Answer

Q19) The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y - 5 = 0 is Show Answer

Q20) A straight line through P
(1, 2) is such that its intercept between the axes is bisected at P. Its equation is Show Answer

Q21) Equation of a line, which is intersecting the X - axis at a distance of 3 units to the left of origin with slope -2, is Show Answer

Q22) Find the equations of the lines, which cut off intercepts on the axes whose sum and product are 1 and -6, respectively. Show Answer

Q23) Let PS be the median of the triangle with vertices P (2, 2), Q (6, -1) and R (7, 3). The equation of the line passing through (1, -1) and parallel to PS is Show Answer

Q24) Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2,2). Show Answer

Q25) A ray of light passing through the point (1,2) reflects on the X - axis at point A and the reflected ray passes through the point (5,3). Find coordinates of A. Show Answer

Q26) Find the equation of the line passing through the point (5,2) and perpendicular to the line joining the points ( 2,3) and (3,-1). Show Answer

Q27) Find the equation of the line passing through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7. Show Answer

Q28) The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is Show Answer

Q29) Find equation of the line passing through the point (2,2) and cutting off intercepts the axes whose sum is 9. Show Answer

Q30) The equation of the straight line joining the origin to the point of intersection of y - x + 7 = 0 and y + 2x - 2 = 0, is Show Answer

Q31) A line perpendicular to the line segment joining the points (1,0) and (2,3) divides it in the ratio 1 : n. Find the equation of the line. Show Answer

Q32) The equation of straight line through the intersection of the lines x - 2y = 1 and x + 3y = 2 and parallel to 3x + 4y = 0, is Show Answer

Q33) A line passes through (2,2) and is perpendicular to the line 3x + y = 3. Its y-intercept is Show Answer

Q34) The line through the points (h,3) and (4,1) intersects the line 7x -9y - 19 = 0 at right angle. Find the value of h. Show Answer

Q35) The inclination of the straight line passing through the point (-3,6) and the mid-point of the line joining the points (4,-5) and ( -2,9) is Show Answer

Q36) Distance between the lines 5x + 3y - 7 = 0 and 15x + 9y + 14 = 0 is Show Answer

Q37) The distance of the point of intersection of lines 2x - 3y + 5 = 0 and 3x + 4y = 0 from the line 5x - 2y = 0 is Show Answer

Q38) The coordinates of the foot of perpendicular from the point (2,3) on the line y = 3x + 4 is given by Show Answer

Q39) A point equidistant from the lines 4x + 3y + 10 = 0, 5x - 12y + 26 = 0 and 7x + 24y - 50 = 0 is Show Answer

Q40) The distance of the point (3, 5) from the line 2x + 3y - 14 = 0 measured parallel to line x - 2y = 1, is Show Answer

Q41) Equation of the line passing through (1,2) and parallel to the line y = 3x - 1 is Show Answer

Q42) The equation of the bisector of the acute angle between the lines 3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 is Show Answer

Q43) The equation of bisectors of the angles between the lines |x| = |y| are Show Answer

Q44) Equation of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are Show Answer

Q45) Lines 2x + y = 1 and 2x + y = 7 are Show Answer

Q46) Two vertices of a triangle are ( 5, -1) and ( -2, 3). If the orthocentre of the triangle is the origin, then coordinates of third vertex are Show Answer

Q47) Orthocentre of triangle with vertices (0,0), (3,4) and (4,0) is Show Answer

Q48) The point moves such that the area of the triangle formed by it with the points (1,5) and (3, -7) is 21 sq units. The locus of the point is Show Answer

Q49) If 5a + 4b + 20c = t, then the value of t for which the line ax + by + c - 1 = 0 always passes through a fixed point is Show Answer

Q50) If the distance of any point (x,y) from the origin is defined as d ( x, y) = max { | x | , | y | }, d ( x,y) = a, non- zero constant, then the locus is a Show Answer

Q51) One diagonal of a square is along the line 8x - 15y = 0 and one of its vertex is (1,2). Then, the equations of the sides of the square passing through this vertex are Show Answer

Q52) A light ray coming along the line 3x + 4y = 5 gets reflected from the line ax + by = 1 and goes along the line 5x - 12y = 10. Then, Show Answer

Q53) The straight lines 4ax + 3by + c = 0, where a + b + c = 0, are concurrent at the point Show Answer

Q54) Two sides of a triangle are the lines (a+b) x + (a-b) y - 2ab = 0
and (a-b)x + (a+b)y - 2ab = 0. If the triangle is isosceles and the third side passes through point (b-a, a-b), then the equation of third side can be Show Answer

Q55) Consider the straight lines x + 2y + 4 = 0 and 4x + 2y - 1= 0. The line 6x + 6y + 7 = 0 is Show Answer

Q56) The equation of line L is Show Answer

Q57) Area formed by the line L with coordinate axis is Show Answer

Q58) Consider a, b and c are variables.
Statement I Such that 3a + 2b + 4c = 0, then the family of lines given by ax + by + c = 0 pass through a fixed point (3,2).
Statement II The equation ax + by + c = 0 will represent a family of straight line passing through a fixed point iff there exists a linear relation between a, b and c. Show Answer

Q59) Statement I Each point on the line y - x + 12 = 0 is equidistant from the lines 4y + 3x - 12 = 0, 3y + 4x - 24 = 0.
Statement II The locus of a point which is equidistant from two given lines is the angular bisector of the two lines.

Q60) The lines x + y = | a | and ax - y = 1 intersect each other in the first quadrant. Then, the set of all possible values of a in the interval Show Answer

Q61) The perpendicular bisector of the line segment joining P(1,4) and Q (k,3) has y-intercept -4. Then, a possible value of k is Show Answer

Q62) A straight line through the point A ( 3,4) is such that is intercept between the axis is bisected at A. Its equation is Show Answer

Q63) The equation of the bisector of the acute angles between the lines 3x - 4y + 7 = 0 and 12x + 5y - 2 = 0 is Show Answer

Q64) The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is -1, is Show Answer

Q65) Equation of the straight line making equal intercepts on the axes and passing through the point ( 2 , 4 ), is Show Answer

Q66) The equation of the line which is such that the portion of line segment intercepted between the coordinate axes is bisected at ( 4 , - 3) , is Show Answer

Q67) If P is length of the perpendicular from origin on the line whose intercepts on the axes are a and b , then Show Answer

Q68) The equation of the line bisecting perpendicularly the segment joining the points ( - 4 , 6 ) and (8 , 8) , is Show Answer

Q69) If a line passes through the point ( 2 , 2 ) and encloses a triangle of area A square units with the coordinate axes, then the intercepts made by the line on the coordinate axes are the roots of the equations Show Answer

Q70) In the above question the coordinates of the other two vertices are Show Answer

Q71) L is variable line such that the algebraic sum of the distances of the points ( 1, 1) , ( 2, 0 ) and ( 0 , 2 )
from the line is equal to zero. The line L will always pass through Show Answer

Q72) The orthocenter of the triangle formed by (0, 0) , (8, 0) , ( 4 , 6) is Show Answer

Q73) The number of the straight lines which are equally inclined to both the exes, is Show Answer

Q74) If A ( 2 , -1 ) and B( 6, 5 ) are two points, then the ratio in which the foot of the perpendicular from ( 4 , 1 ) to AB divided it , is Show Answer

Q75) If A and B are two fixed points, then the locus of a point which moves in such a way that the angle APB is a right angle is Show Answer

Q76) The vertices of a triangle are ( 0 , 3 ) ( -3 , 0 ) and ( 3 , 0 ) . The coordinates of its orthocentre are Show Answer

Q77) Points A ( 1 , 3 ) & C ( 5 , 1 ) are opposite vertices of a rectangle ABCD. If slope of BD is 2, then its equation is Show Answer

Q78) P ( 2 , 1 ),Q ( 4 ,- 1 ), R ( 3 , 2 ) are the vertices of a triangle and if through P and R lines parallel to opposite sides are drawn to intersect in S, then the area of PQRS is Show Answer

Q79) If foot of perpendicular from origin to a straight line is at point ( 3 , -4 ). Then, equation of the line is Show Answer

Q80) Two points A and B move on the coordinate axes such that the distance between them remains same. The locus of the mid-point of AB is Show Answer

Q81) The equation of line through the point ( 1 , 2 ) whose distance from the point ( 3, 1 ) has the greatest value, is Show Answer

Q82) In a rhombus ABCD the diagonals AC and BD intersect at the point ( 3 ,4 ). If the point A is ( 1 ,2 ) the diagonal BD has the equation Show Answer

Q83) The equation to the bisecting join of ( 3 ,- 4 ) & ( 5 ,2 ) & having its intercepts on x-axis & the y-axis in the ratio 2:1 is Show Answer

Q84) A(-5 ,0) and B(3, 0) are two of the vertices of a triangle ABC. Its area is 20 square cms. The vertex C lies on the line x - y = 2. The coordinates of C are Show Answer

Q85) An equation of st. line which passes through point (1, -2) & cuts off equal intercepts from axes will be Show Answer

Q86) The coordinates of three vertices of a quadrilateral in order are (6 ,1),(7, 2) and (-1 ,0). If the area of the quadrilateral is 4 square units, then the locus of the fourth vertex is Show Answer

Q87) Two points (a ,0) and (0, b) are joined by a straight line. Another point on this line, is Show Answer

Q88) The equation of line bisecting perpendicularly the segment joining the points (-4 ,6) and (8, 8), is Show Answer

Q89) A triangle ABC, right angled at A, has points A& B as (2, 3) & (0, -1) respectively. If BC = 5 units, then point C, is Show Answer

Q90) A ray of light passing through the point (1,2) is reflected on the x-axis at a point P and passes through the point (5, 3), then the abscissa of a point P is Show Answer

Q91) The area of the triangle formed by y-axis, the straight line L passing through (1 ,1) and (2 ,0) and the straight line perpendicular to the line L and passing through (1/2 ,0) Show Answer

Q92) If sum of distances from a point P on two mutually perpendicular straight lines is 1 unit, then locus of P is Show Answer

Q93) A line has slope m and y - intercept 4. The distance between the origin and the line is equal to Show Answer

Q94) The orthocenter of the triangle whose vertices are (5 ,-2),(-1 ,2) and (1 ,4), is Show Answer

Q95) Orthocenter of triangle with vertices (0, 0), (3, 4) and (4, 0) is Show Answer

Q96) The equation of the straight lines passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is -1, is Show Answer