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Straight Lines and Pair of Straight Lines

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  1. 151.Let A be a fixed point (0,6) and B be a moving point (2t,0).
  2. 152.Let ABC be a triangle with A(-3,1) and ACB=, 0<<2.
  3. 153.If p and q are the lengths of the perpendiculars from the origin on the lines, x - y = k2 …
  4. 154.Let A(1,0), B(6,2) and C(32,6) be the vertices of a triangle ABC.
  5. 155.The locus of the mid-points of the perpendiculars drawn from points on the line, x=2y to t…
  6. 156.Let C be the centroid of the triangle with vertices (3,-1), (1,3) and (2,4).
  7. 157.If a ABC has vertices A(-1,7), B(-7,1) and C(5,-5), then its orthocentre has coordinates:
  8. 158.A triangle ABC lying in the first quadrant has two vertices as A(1,2) and B(3,1).
  9. 159.If the perpendicular bisector of the line segment joining the points P(1,4) and Q(k,3) has…
  10. 160.If the line 2x-y+3=0 is at a distance 1√5 and 2√5 from the lines 4x-2y+=0 and 6x-3y+=0, re…
  11. 161.*(This question, "Let f: R R...", is from Continuity and Differentiability, not Straight L…
  12. 162.Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively.
  13. 163.Consider the set of all lines px+qy+r=0 such that 3p+2q+4r=0.
  14. 164.Let the equations of two sides of a triangle be 3x-2y+6=0 and 4x+5y-20=0.
  15. 165.A point P moves on the line 2x-3y+4=0.
  16. 166.If the line 3x+4y-24=0 intersects the x-axis at the point A and the y-axis at the point B,…
  17. 167.Two vertices of a triangle are (0,2) and (4,3).
  18. 168.Two sides of a parallelogram are along the lines, x+y=3 and x-y+3=0.
  19. 169.If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1,2),(3,4) and…
  20. 170.If a straight line passing through the point P(-3,4) is such that its intercepted portion …
  21. 171.If the straight line, 2x-3y+17=0 is perpendicular to the line passing through the points (…
  22. 172.Let O(0,0) and A(0,1) be two fixed points.
  23. 173.Slope of a line passing through P(2,3) and intersecting the line x+y=7 at a distance of 4 …
  24. 174.Two vertical poles of heights, 20m and 80m stand apart on a horizontal plane.
  25. 175.Suppose that the points (h,k), (1,2) and (-3,4) lie on the line L_1.
  26. 176.If the two lines x+(a-1)y=1 and 2x+a^2y=1 (a R-0,1) are perpendicular, then the distance o…
  27. 177.A rectangle is inscribed in a circle with a diameter lying along the line 3y=x+7.
  28. 178.A triangle has a vertex at (1,2) and the mid points of the two sides through it are (-1,1)…
  29. 179.A straight line L at a distance of 4 units from the origin makes positive intercepts on th…
  30. 180.The equation y= x(x+2)-^2(x+1) represents a straight line lying in:
  31. 181.Let the orthocentre and centroid of a triangle be A(-3,5) and B(3,3) respectively.
  32. 182.A straight line through a fixed point (2,3) intersects the coordinate axes at distinct poi…
  33. 183.In a triangle ABC, coordinates of A are (1,2) and the equations of the medians through B a…
  34. 184.The foot of the perpendicular drawn from the origin, on the line, 3x+y= (0) is P.
  35. 185.The sides of a rhombus ABCD are parallel to the lines, x-y+2=0 and 7x-y+3=0.
  36. 186.A square, of each side 2, lies above the x-axis and has one vertex at the origin.
  37. 187.A ray of light is incident along a line which meets another line, 7x-y+1=0, at the point (…
  38. 188.Two sides of a rhombus are along the lines, x-y+1=0 and 7x-y-5=0.
  39. 189.If a variable line drawn through the intersection of the lines x3+ y4=1 and x4+ y3=1, meet…
  40. 190.The point (2,1) is translated parallel to the line L: x-y=4 by 2√3 units.
  41. 191.A straight line through origin O meets the lines 3y=10-4x and 8x+6y+5=0 at points A and B …
  42. 192.Let L be the line passing through the point P(1,2) such that its intercepted segment betwe…
  43. 193.The points (0,83), (1,3) and (82,30):
  44. 194.A straight line L through the point (3,-2) is inclined at an angle of 60^ to the line √3x+…
  45. 195.The circum centre of a triangle lies at the origin and its centroid is the mid point of th…
  46. 196.Given three points P, Q, R with P(5,3) and R lies on the x-axis.
  47. 197.If a line intercepted between the coordinate axes is trisected at a point A(4,3), which is…
  48. 198.Let a,b,c and d be non-zero numbers.
  49. 199.Let PS be the median of the triangle with vertices P(2,2), Q(6,-1) and R(7,3).
  50. 200.If the three distinct lines x+2ay+a=0, x+3by+b=0 and x+4ay+a=0 are concurrent, then the po…