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Straight Lines and Pair of Straight Lines

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  1. 101.The equations of two sides of a variable triangle are x=0 and y=3, and its third side is a…
  2. 102.A triangle is formed by X-axis, Y-axis and the line 3x+4y=60.
  3. 103.A light ray emits from the origin making an angle 30^ with the positive x-axis.
  4. 104.Let B and C be two points on the line y+x=0 such that B and C are symmetric with respect t…
  5. 105.A triangle is formed by the tangents at the point (2,2) on the curves y^2=2x and x^2+y^2=4…
  6. 106.A straight line cuts off the intercepts OA=a and OB=b on the positive directions of x-axis…
  7. 107.If the orthocentre of the triangle, whose vertices are (1,2),(2,3) and (3,1) is (,), then …
  8. 108.The equation of the angle bisectors of the lines represented by the equation 2x^2+xy-3y^2=…
  9. 109.Let A(0,1), B(1,1) and C(1,0) be the mid-points of the sides of a triangle with incentre a…
  10. 110.Let A be the point (1,2) and B be any point on the curve x^2+y^2=16.
  11. 111.Let the equations of two adjacent sides of a parallelogram ABCD be 2x-3y=-23 and 5x+4y=23.
  12. 112.From the top A of a vertical wall AB of height 30m, the angles of depression of the top P …
  13. 113.The angle of elevation of the top P of a tower from the feet of one person standing due So…
  14. 114.Let A(3 a, a), a>0, be a fixed point in the xy-plane.
  15. 115.Let the area of the triangle with vertices A(1,), B(,0) and C(0,) be 4 sq.
  16. 116.Let R be the point (3,7) and let P and Q be two points on the line x+y=5 such that PQR is …
  17. 117.In an isosceles triangle ABC, the vertex A is (6,1) and the equation of the base BC is 2x+…
  18. 118.A rectangle R with end points of one of its sides as (1,2) and (3,6) is inscribed in a cir…
  19. 119.A ray of light passing through the point P(2,3) reflects on the x-axis at point A and the …
  20. 120.Let a triangle be bounded by the lines L_1: 2x+5y=10; L_2: -4x+3y=12 and the line L_3, whi…
  21. 121.The distance between the two points A and A' which lie on y=2 such that both the line segm…
  22. 122.The distance of the origin from the centroid of the triangle whose two sides have the equa…
  23. 123.Let AB and PQ be two vertical poles, 160m apart from each other.
  24. 124.From the base of a pole of height 20 meter, the angle of elevation of the top of a tower i…
  25. 125.A line, with the slope greater than one, passes through the point A(4,3) and intersects th…
  26. 126.Let the point P(,) be at a unit distance from each of the two lines L_1: 3x-4y+12=0, and L…
  27. 127.A point P moves so that the sum of squares of its distances from the points (1,2) and (-2,…
  28. 128.The equations of the sides AB, BC and CA of a triangle ABC are 2x+y=0, x+py=15a and x-y=3 …
  29. 129.Let A(1,1), B(-4,3), C(-2,-5) be vertices of a triangle ABC, P be a point on side BC, and …
  30. 130.The equations of the sides AB, BC and CA of a triangle ABC are 2x+y=0, x+py=39 and x-y=3 r…
  31. 131.For t(0,2), if ABC is an equilateral triangle with vertices A( t,- t), B( t, t) and C(a,b)…
  32. 132.Let the circumcentre of a triangle with vertices A(a,3), B(b,5) and C(a,b), ab>0 be P(1,1)…
  33. 133.Let m_1, m_2 be the slopes of two adjacent sides of a square of side a such that a^2+11a+3…
  34. 134.Let A(,-2), B(,6) and C(4,-2) be vertices of a ABC.
  35. 135.A tower PQ stands on a horizontal ground with base Q on the ground.
  36. 136.Let a vertical tower AB of height 2h stands on a horizontal ground.
  37. 137.The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on …
  38. 138.A horizontal park is in the shape of a triangle OAB with AB=16.
  39. 139.The angle of elevation of the top of a tower from a point A due north of it is and from a …
  40. 140.The intersection of three lines x-y=0, x+2y=3 and 2x+y=6 is a:
  41. 141.If the curve x^2+2y^2=2 intersects the line x+y=1 at two points P and Q, then the angle su…
  42. 142.The image of the point (3,5) in the line x-y+1=0, lies on:
  43. 143.A man is walking on a straight line.
  44. 144.Let A(-1,1), B(3,4) and C(2,0) be given three points.
  45. 145.In a PQR, the coordinates of the points P and Q are (-2,4) and (4,-2), respectively.
  46. 146.The number of integral values of m, so that the abscissa of point of intersection of lines…
  47. 147.The equation of one of the straight lines which passes through the point (1,3) and makes a…
  48. 148.Consider a triangle having vertices A(-2,3), B(1,9) and C(3,8).
  49. 149.Let the equation of the pair of lines, y=px and y=qx can be written as (y-px)(y-qx)=0.
  50. 150.Two sides of a parallelogram are along the lines 4x+5y=0 and 7x+2y=0.