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Trigonometric Ratios and Identities

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  1. 101.Let the circle S:36x^2+36y^2-108x+120y+C=0 be such that it neither intersects nor touches …
  2. 102.Let y=mx+c, m>0 be the focal chord of y^2=-64x, which is tangent to (x+10)^2+y^2=4.
  3. 103.Let E be an ellipse whose axes are parallel to the coordinate axes, having its centre at (…
  4. 104.Let T be the tangent to the ellipse E:x^2+4y^2=5 at the point P(1,1).
  5. 105.Let a line L:2x+y=k, k>0 be a tangent to the hyperbola x^2-y^2=3.
  6. 106.Let B be the centre of the circle x^2+y^2-2x+4y+1=0.
  7. 107.Two circles each of radius 5 units touch each other at the point (1,2).
  8. 108.The locus of a point, which moves such that the sum of squares of its distances from the p…
  9. 109.A tangent line L is drawn at the point (2,-4) on the parabola y^2=8x.
  10. 110.If two tangents drawn from a point P to the parabola y^2=16(x-3) are at right angles, then…
  11. 111.If the minimum area of the triangle formed by a tangent to the ellipse x^2b^2+y^24a^2=1 an…
  12. 112.If one end of a focal chord AB of the parabola y^2=8x is at A(12,-2), then the equation of…
  13. 113.Let a line y=mx (m>0) intersect the parabola y^2=x at a point P, other than the origin.
  14. 114.Let the line y=mx and the ellipse 2x^2+y^2=1 intersect at a point P in the first quadrant.
  15. 115.The circle passing through the intersection of the circles x^2+y^2-6x=0 and x^2+y^2-4y=0, …
  16. 116.The number of integral values of k for which the line 3x+4y=k intersects the circle x^2+y^…
  17. 117.If the common tangent to the parabolas y^2=4x and x^2=4y also touches the circle x^2+y^2=c…
  18. 118.Let P(3,3) be a point on the hyperbola x^2a^2-y^2b^2=1.
  19. 119.If a circle of radius R passes through the origin O and intersects the coordinate axes at …
  20. 120.Let C_1 and C_2 be the centres of the circles x^2+y^2-2x-2y-2=0 and x^2+y^2-6x-6y+14=0 res…
  21. 121.A square is inscribed in the circle x^2+y^2-6x+8y-103=0 with its sides parallel to the coo…
  22. 122.If a circle C passing through the point (4,0) touches the circle x^2+y^2+4x-6y=12 external…
  23. 123.The equation of a tangent to the parabola x^2=8y, which makes an angle with the positive d…
  24. 124.Equation of a common tangent to the circle x^2+y^2-6x=0 and the parabola y^2=4x, is:
  25. 125.If tangents are drawn to the ellipse x^2+2y^2=2 at all points on the ellipse other than it…
  26. 126.The equation of a tangent to the hyperbola 4x^2-5y^2=20 parallel to the line x-y=2 is:
  27. 127.If a tangent to the circle x^2+y^2=1 intersects the coordinate axes at distinct points P a…
  28. 128.If y=mx+4 is a tangent to both the parabolas y^2=4x and x^2=2by, then b is equal to:
  29. 129.If the tangents on the ellipse 4x^2+y^2=8 at the points (1,2) and (a,b) are perpendicular …
  30. 130.The tangent to the parabola y^2=4x at the point where it intersects the circle x^2+y^2=5 i…
  31. 131.The tangent and normal to the ellipse 3x^2+5y^2=32 at the point P(2,2) meet the x-axis at …
  32. 132.If the tangent to the parabola y^2=x at a point (,), (>0) is also a tangent to the ellipse…
  33. 133.Let P be the point of intersection of the common tangents to the parabola y^2=12x and hype…
  34. 134.The equation of a common tangent to the curves y^2=16x and xy=-4, is:
  35. 135.The locus of the point of intersection of the lines √2x-y+4√2k=0 and √2kx+ky-4√2=0 (k is a…
  36. 136.Tangent and normal are drawn at P(16,16) on the parabola y^2=16x, which intersect the axis…
  37. 137.If the tangent at (1,7) to the curve x^2=y-6 touches the circle x^2+y^2+16x+12y+c=0 then t…
  38. 138.Tangents are drawn to the hyperbola 4x^2-y^2=36 at the points P and Q.
  39. 139.If two parallel chords of a circle, having diameter 4 units, lie on opposite sides of the …
  40. 140.If y=mx+c is the normal at a point on the parabola y^2=8x whose focal distance is 8 units,…
  41. 141.If the common tangents to the parabola x^2=4y and the circle x^2+y^2=4 intersect at the po…
  42. 142.The locus of the point of intersection of the straight lines tx-2y-3t=0 and x-2ty+3=0 (t R…
  43. 143.The number of common tangents to the circles x^2+y^2-4x-6y-12=0 and x^2+y^2+6x+18y+26=0 is…
  44. 144.Let the tangents drawn to the circle x^2+y^2=16 from the point P(0,h) meet the x-axis at p…
  45. 145.Let PQ be a double ordinate of the parabola y^2=-4x, where P lies in the second quadrant.
  46. 146.The set of all real values of for which exactly two common tangents can be drawn to the ci…
  47. 147.If the point (1,4) lies inside the circle x^2+y^2-6x-10y+P=0 and the circle does not touch…
  48. 148.Two tangents are drawn from a point (-2,-1) to the curve y^2=4x.
  49. 149.The locus of the foot of perpendicular drawn from the centre of the ellipse x^2+3y^2=6 on …
  50. 150.The tangent at an extremity (in the first quadrant) of the latus rectum of the hyperbola x…