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Trigonometric Ratios and Identities

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  1. 51.Let A and B be the two points of intersection of the line y+5=0 and the mirror image of th…
  2. 52.Let the line x+y=1 meet the circle x^2+y^2=4 at the points A and B.
  3. 53.Let Y=Y(X) be a curve lying in the first quadrant such that the area enclosed by the tange…
  4. 54.Equations of two diameters of a circle are 2x-3y=5 and 3x-4y=7.
  5. 55.If the circles (x+1)^2+(y+2)^2=r^2 and x^2+y^2-4x-4y+4=0 intersect at exactly two distinct…
  6. 56.If the points of intersection of two distinct conics x^2+y^2=4b and (a second conic, not p…
  7. 57.Let P be a point on a hyperbola H (equation not preserved) in the first quadrant such that…
  8. 58.Let the line L:√2x+y= pass through the point of intersection P (in the first quadrant) of …
  9. 59.Let be the area of the region (x,y) R^2: x^2+y^221, y^24x, x1.
  10. 60.Points P(-3,2), Q(9,10), and R(,4) lie on a circle C with PR as its diameter.
  11. 61.Let the tangents at the points A(4,-11) and B(8,-5) on the circle x^2+y^2-3x+10y-15=0 inte…
  12. 62.A circle with centre (2,3) and radius 4 intersects the line x+y=3 at the points P and Q.
  13. 63.Let a circle C_1 be obtained by rolling the circle x^2+y^2-4x-6y+11=0 upwards 4 units alon…
  14. 64.Let a tangent to the curve 9x^2+16y^2=144 intersect the coordinate axes at points A and B.
  15. 65.Let A be a point on the x-axis.
  16. 66.The line x=8 is the directrix of the ellipse E:x^2a^2+y^2b^2=1 with corresponding focus (2…
  17. 67.A circle passing through the point P(,) in the first quadrant touches the two coordinate a…
  18. 68.If the tangents at the points P and Q on the circle x^2+y^2-2x+y=5 meet at the point R(94,…
  19. 69.Let O be the origin and OP,OQ be tangents to the circle x^2+y^2-6x+4y+8=0 at points P,Q on…
  20. 70.The number of common tangents to the circles x^2+y^2-18x-15y+131=0 and x^2+y^2-6x-6y-7=0 i…
  21. 71.Let x-2y= be a tangent to the hyperbola a^2x^2-y^2=b^2.
  22. 72.If two tangents drawn from a point (,) lying on the ellipse 25x^2+4y^2=1 to the parabola y…
  23. 73.Let a line L_1 be tangent to the hyperbola x^216-y^24=1, and let L_2 be the line through t…
  24. 74.Let a circle C of radius 5 lie below the x-axis.
  25. 75.If y=m_1x+c_1 and y=m_2x+c_2, m_1 m_2, are two common tangents of the circle x^2+y^2=2 and…
  26. 76.Let the normal at a point on the parabola y^2=6x pass through the point (5,-8).
  27. 77.Let P:y^2=4ax, a>0, be a parabola with focus S.
  28. 78.Let the common tangents to the curves 4(x^2+y^2)=9 and y^2=4x intersect at the point Q.
  29. 79.If m is the slope of a common tangent to the curves x^216+y^29=1 and x^2+y^2=12, then 12m^…
  30. 80.Let the equations of two diameters of a circle x^2+y^2-2x+2fy+1=0 be 2px-y=1 and 2x+py=4p.
  31. 81.Let the tangent drawn to the parabola y^2=24x at the point (,) be perpendicular to the lin…
  32. 82.A common tangent T to the curves C_1:x^24+y^29=1 and C_2:x^242-y^2143=1 does not pass thro…
  33. 83.Let the tangents at two points A and B on the circle x^2+y^2-4x+3=0 meet at origin O(0,0).
  34. 84.Let AB be a chord of length 12 of the circle (x-2)^2+(y+1)^2=1694.
  35. 85.The tangents at the points A(1,3) and B(1,-1) on the parabola y^2-2x-2y=1 meet at the poin…
  36. 86.If the tangents drawn at the points P and Q on the parabola y^2=2x-3 intersect at the poin…
  37. 87.Two tangent lines l_1 and l_2 are drawn from the point (2,0) to the parabola 2y^2=-x.
  38. 88.The acute angle between the pair of tangents drawn to the ellipse 2x^2+3y^2=5 from the poi…
  39. 89.Let a point P be such that its distance from the point (5,0) is thrice the distance of P f…
  40. 90.If the point of intersections of the ellipse x^216+y^2b^2=1 and the circle x^2+y^2=4b, b>4…
  41. 91.For which of the following curves, the line x+√3y=2√3 is the tangent at the point (3√32,12…
  42. 92.A line is a common tangent to the circle (x-3)^2+y^2=9 and the parabola y^2=4x.
  43. 93.A tangent is drawn to the parabola y^2=6x, which is perpendicular to the line 2x+y=1.
  44. 94.If the curve y=ax^2+bx+c, x R, passes through the point (1,2) and the tangent line to this…
  45. 95.The locus of the point of intersection of the lines √3kx+ky-4√3=0 and √3x-y-4√3k=0 is a co…
  46. 96.The minimum distance between any two points P_1 and P_2, where P_1 lies on one circle and …
  47. 97.Let ABCD be a square of side of unit length.
  48. 98.Let a tangent be drawn to the ellipse x^227+y^2=1 at (3√3,), where (0,2).
  49. 99.Consider a hyperbola H:x^2-2y^2=4.
  50. 100.Two tangents are drawn from the point P(-1,1) to the circle x^2+y^2-2x-6y+6=0.