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Straight Lines and Pair of Straight Lines

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  1. 201.The base of an equilateral triangle is along the line given by 3x+4y=9.
  2. 202.The x-coordinate of the incentre of the triangle that has the coordinates of mid points of…
  3. 203.A light ray emerging from the point source placed at P(1,3) is reflected at a point Q in t…
  4. 204.If the three lines x-3y=p, ax+2y=q and ax+y=r form a right-angled triangle then:
  5. 205.A ray of light along x+√3y=√3 gets reflected upon reaching x-axis, the equation of the ref…
  6. 206.If the x-intercept of some line L is double as that of the line, 3x+4y=12 and the y-interc…
  7. 207.If the extremities of the base of an isosceles triangle are the points (2a,0) and (0,a) an…
  8. 208.Let _1 be the angle between two lines 2x+3y+c_1=0 and -x+5y+c_2=0 and _2 be the angle betw…
  9. 209.Let A(-3,2) and B(-2,1) be the vertices of a triangle ABC.
  10. 210.If the image of point P(2,3) in a line L is Q(4,5), then the image of point R(0,0) in the …
  11. 211.If the line 2x+y=k passes through the point which divides the line segment joining the poi…
  12. 212.If the straight lines x+3y=4, 3x+y=4 and x+y=0 form a triangle, then the triangle is:
  13. 213.If two vertical poles 20m and 80m high stand apart on a horizontal plane, then the height …
  14. 214.The point of intersection of the lines (a^3+3)x+ay+a-3=0 and (a^5+2)x+(a+2)y+2a+3=0 (a rea…
  15. 215.If the point (1,a) lies between the straight lines x+y=1 and 2(x+y)=3 then a lies in inter…
  16. 216.If two vertices of a triangle are (5,-1) and (-2,3) and its orthocentre is at (0,0), then …
  17. 217.Let L be the line y=2x, in the two dimensional plane.
  18. 218.The line parallel to x-axis and passing through the point of intersection of lines ax+2by+…
  19. 219.Consider the straight lines L_1: x-y=1, L_2: x+y=1, L_3: 2x+2y=5, L_4: 2x-2y=7.
  20. 220.If a,b,c R and 1 is a root of equation ax^2+bx+c=0, then the curve y=4ax^2+3bx+2c, a0 inte…
  21. 221.If A(2,-3) and B(-2,1) are two vertices of a triangle and third vertex moves on the line 2…
  22. 222.The lines x+y=|a| and ax-y=1 intersect each other in the first quadrant.
  23. 223.The lines L_1: y-x=0 and L_2: 2x+y=0 intersect the line L_3: y+2=0 at P and Q respectively…
  24. 224.The lines p(p^2+1)x-y+q=0 and (p^2+1)^2x+(p^2+1)y+2q=0 are perpendicular to a common line …
  25. 225.The perpendicular bisector of the line segment joining P(1,4) and Q(k,3) has y-intercept -…
  26. 226.Let A(h,k), B(1,1) and C(2,1) be the vertices of a right angled triangle with AC as its hy…
  27. 227.Let P=(-1,0), Q=(0,0) and R=(3,3√3) be three points.
  28. 228.If one of the lines of my^2+(1-m^2)xy-mx^2=0 is a bisector of the angle between the lines …
  29. 229.If (a,a^2) falls inside the angle made by the lines y= x2, x>0 and y=3x, x>0, then a belon…
  30. 230.A straight line through the point A(3,4) is such that its intercept between the axes is bi…
  31. 231.If a vertex of a triangle is (1,1) and the mid points of two sides through this vertex are…
  32. 232.The equation of the straight line passing through the point (4,3) and making intercepts on…
  33. 233.Let A(2,-3) and B(-2,3) be vertices of a triangle ABC.
  34. 234.If one of the lines given by 6x^2-xy+4cy^2=0 is 3x+4y=0, then c equals:
  35. 235.If the sum of the slopes of the lines given by x^2-2cxy-7y^2=0 is four times their product…
  36. 236.If the equation of the locus of a point equidistant from the points (a_1,b_1) and (a_2,b_2…
  37. 237.Locus of centroid of the triangle whose vertices are (a t,a t), (b t,-b t) and (1,0), wher…
  38. 238.If x_1,x_2,x_3 and y_1,y_2,y_3 are both in G.P.
  39. 239.A square of side a lies above the x-axis and has one vertex at the origin.
  40. 240.If the pair of straight lines x^2-2pxy-y^2=0 and x^2-2qxy-y^2=0 be such that each pair bis…
  41. 241.A triangle with vertices (4,0),(-1,-1),(3,5) is:
  42. 242.Locus of mid point of the portion between the axes of x+y=p where p is constant is:
  43. 243.The pair of lines represented by 3ax^2+5xy+(a^2-2)y^2=0 are perpendicular to each other fo…
  44. 244.If the pair of lines ax^2+2hxy+by^2+2gx+2fy+c=0 intersect on the y-axis then:
  45. 245.Among the statements: (S1): If A(5,-1) and B(-2,3) are two vertices of a triangle, whose o…
  46. 246.If the pair of lines [ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0] intersect on the y-axis then…
  47. 247.Locus of mid point of the portion between the axes of x cos [ + y, = p] where p is constan…
  48. 248.If the sum of the slopes of the lines given by x^2 - 2cxy - 7y^2 = 0 is four times their p…
  49. 249.If one of the lines given by 6x^2 - xy + 4cy^2 = 0 is 3x + 4y = 0, then c equals :
  50. 250.Let [A( 2, - 3 )] and [B( -2, 1 )] be vertices of a triangle ABC.