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Straight Lines and Pair of Straight Lines

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  1. 51.The straight lines l_1 and l_2 pass through the origin and trisect the line segment of the…
  2. 52.A point on the straight line, 3x + 5y = 15 which is equidistant from the coordinate axes w…
  3. 53.From the point (-1,-1), two rays are sent making angles of 45^ with the line x+y=0.
  4. 54.Let A,B be points on the two half-lines x-√3|y|= , >0 at a distance of from their point of…
  5. 55.Let the distance between two parallel lines be 5 units and a point P lie between the lines…
  6. 56.Let a ray of light passing through the point (3,10) reflects on the line 2 x+y=6 and the r…
  7. 57.If the orthocentre of the triangle formed by the lines 2 x+3 y-1=0, x+2 y-1=0 and a x+b y-…
  8. 58.Let ABC be an isosceles triangle in which A is at (-1,0),=(2 )/(3),AB=AC and B is on the p…
  9. 59.The lines L_1,L_2, ,L_20 are distinct.
  10. 60.Let A(-2,-1),B(1,0),C( , ) and D( , ) be the vertices of a parallelogram ABCD.
  11. 61.If the sum of squares of all real values of , for which the lines 2x-y+3=0,6x+3y+1=0 and x…
  12. 62.If the line l_1:3y-2x=3 is the angular bisector of the lines l_2:x-y+1=0 and l_3: x+ y+17=…
  13. 63.Let the equations of two adjacent sides of a parallelogram ABCD be 2x-3y=-23 and 5x+4y=23.
  14. 64.Let the equation of the circle, which touches the x-axis at the point (a,0), a>0, and cuts…
  15. 65.The equations of the sides AB and AC of a triangle ABC are (+1)x+ y=4 and x+(1-)y+=0 respe…
  16. 66.If the x-intercept of a focal chord of the parabola y^2=8x+4y+4 is 3, then the length of t…
  17. 67.Two circles in the first quadrant of radii r_1 and r_2 touch the coordinate axes.
  18. 68.If the circle x^2+y^2-2gx+6y-19c=0, g,c R passes through the point (6,1) and its centre li…
  19. 69.If P is a point on the parabola y=x^2+4 which is closest to the straight line y=4x-1, then…
  20. 70.Let P be a variable point on the parabola y=4x^2+1.
  21. 71.Let PQ be a diameter of the circle x^2+y^2=9.
  22. 72.Let P be a point on the parabola y^2=12x and N be the foot of the perpendicular drawn from…
  23. 73.The chord PQ of the parabola y^2=x, where one end P of the chord is at the point (4,-2), i…
  24. 74.The shortest distance between the line y-x=1 and the curve x=y^2 is:
  25. 75.From the point (-1,-1), two rays are sent making angles of 45^ with the line x+y=0.
  26. 76.A rectangle is formed by the lines x=0, y=0, x=3 and y=4.
  27. 77.Let A(1,0), B(2,-1) and C(73,43) be three points.
  28. 78.Let the angles made with the positive x-axis by two straight lines drawn from the point P(…
  29. 79.Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the l…
  30. 80.Let the mid points of the sides of a triangle ABC be (52,7), (52,3) and (4,5).
  31. 81.Let the line L_1: x+3=0 intersect the lines L_2: x-y=0 and L_3: 3x+y=0 at the points A and…
  32. 82.If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and 3x+4…
  33. 83.Let the distance between two parallel lines be 5 units and a point P lie between the lines…
  34. 84.Let the triangle PQR be the image of the triangle with vertices (1,3),(3,1) and (2,4) in t…
  35. 85.A rod of length eight units moves such that its ends A and B always lie on the lines x-y+2…
  36. 86.Let the line x+y=1 meet the axes of x and y at A and B, respectively.
  37. 87.A line passes through the origin and makes equal angles with the positive coordinate axes.
  38. 88.Let ABC be a triangle formed by the lines 7x-6y+3=0, x+2y-31=0 and 9x-2y-19=0.
  39. 89.Let the three sides of a triangle be on the lines 4x-7y+10=0, x+y=5 and 7x+4y=15.
  40. 90.Let ABC be the triangle such that the equations of lines AB and AC be 3y-x=2 and x+y=2, re…
  41. 91.A line passing through the point P(a,0) makes an acute angle with the positive x-axis.
  42. 92.Let a be the length of a side of a square OABC with O being the origin.
  43. 93.The portion of the line 4x+5y=20 in the first quadrant is trisected by the lines L_1 and L…
  44. 94.Let A and B be two finite sets with m and n elements respectively.
  45. 95.In a ABC, suppose y=x is the equation of the bisector of the angle B and the equation of t…
  46. 96.Let (5, a4) be the circumcenter of a triangle with vertices A(a,-2), B(a,6) and C( a4,-2).
  47. 97.The distance of the point (2,3) from the line 2x-3y+28=0, measured parallel to the line √3…
  48. 98.If x^2-y^2+2hxy+2gx+2fy+c=0 is the locus of a point, which moves such that it is always eq…
  49. 99.Let A(a,b), B(3,4) and (-6,-8) respectively denote the centroid, circumcentre and orthocen…
  50. 100.Let PQR be a triangle.