questionrEarly access

Circle

Showing 50 of 219 · 219 total
  1. 51.The number of common tangents, to the circles x^2+y^2-18 x-15 y+131=0 and x^2+y^2-6 x-6 y-…
  2. 52.Let the centre of a circle C be ( , ) and its radius r<8.
  3. 53.Let A be the point (1,2) and B be any point on the curve x^2+y^2=16.
  4. 54.A line segment AB of length moves such that the points A and B remain on the periphery of …
  5. 55.Let O be the origin and OP and OQ be the tangents to the circle x^2+y^2-6x+4y+8=0 at the p…
  6. 56.If the tangents at the points P and Q on the circle x^2+y^2-2x+y=5 meet at the point R((9)…
  7. 57.The set of all values of a^2 for which the line x+y=0 bisects two distinct chords drawn fr…
  8. 58.The locus of the centres of the circles, which touch the circle, x2 + y2 = 1 externally, a…
  9. 59.A square is inscribed in the circle x2 + y2 -- 6x + 8y -- 103 = 0 with its sides parallel …
  10. 60.Let PQ and MN be two straight lines touching the circle x^2+y^2-4x-6y-3=0 at the points A …
  11. 61.Let y=x (in the closed half-plane x0) be the equation of a chord of the circle C_1 of diam…
  12. 62.Suppose two chords are drawn from the point P(1,2) on the circle x^2+y^2+x-3y=0, and each …
  13. 63.Let C be a circle having centre in the first quadrant and touching the x-axis at a distanc…
  14. 64.Let a circle C have its centre in the first quadrant, pass through the origin (so it meets…
  15. 65.Consider the circle C: x^2+y^2-6x-8y-11=0.
  16. 66.Let the ellipse E:x^24/3+y^24/P=1 pass through the centre of the circle C: x^2+y^2-2x-4y-1…
  17. 67.Let y^2=12x have focus S, and let PQ be a focal chord such that SP SQ=1474.
  18. 68.Let r be the radius of the circle which touches the x-axis at the point (a,0), a<0, and th…
  19. 69.Let the circle C touch the line x-y+1=0, have its centre on the positive x-axis, and cut o…
  20. 70.A circle C of radius 2 lies in the second quadrant and touches both coordinate axes.
  21. 71.Let circle C' be the image of C: x^2+y^2-2x+4y-4=0 in the line 2x-3y+5=0.
  22. 72.If the four distinct points (4,6),(-1,5),(0,0) and (k,3k) lie on a circle of radius r, the…
  23. 73.Let C_1 be the circle in the third quadrant of radius 3 that touches both coordinate axes.
  24. 74.The area (in square units) of the part of circle x^2+y^2=169 which is below the line 5x-y=…
  25. 75.Four distinct points (2k,3k),(1,0),(0,1) and (0,0) lie on a circle for k equal to:
  26. 76.If one of the diameters of the circle x^2+y^2-10x+4y+13=0 is a chord of another circle C, …
  27. 77.Let a variable line passing through the centre of the circle x^2+y^2-16x-4y=0 meet the pos…
  28. 78.If the shortest distance of the parabola y^2=4x from the centre of the circle x^2+y^2-4x-1…
  29. 79.The locus of the midpoints of the chords of the circle C_1:(x-4)^2+(y-5)^2=4, which subten…
  30. 80.The points of intersection of the line ax+by=0 (a b) and the circle x^2+y^2-2x=0 are A(,0)…
  31. 81.Let y=x+2, 4y=3x+6, and 3y=4x+1 be three tangent lines to the circle (x-h)^2+(y-k)^2=r^2.
  32. 82.Let P(a_1,b_1) and Q(a_2,b_2) be two distinct points on a circle with centre C(√2,√3).
  33. 83.The set of all values of a^2 for which the line x+y=0 bisects two distinct chords drawn fr…
  34. 84.If the area bounded by the curve 2y^2=3x, the lines x+y=3, y=0, and outside the circle (x-…
  35. 85.Let a circle C:(x-h)^2+(y-k)^2=r^2, k>0, touch the x-axis at (1,0).
  36. 86.Let a circle C touch the lines L_1:4x-3y+K_1=0 and L_2:4x-3y+K_2=0, K_1,K_2 R.
  37. 87.Let the abscissae of the two points P and Q be the roots of 2x^2-rx+p=0, and the ordinates…
  38. 88.A circle touches both the y-axis and the line x+y=0.
  39. 89.Let C be a circle passing through the points A(2,-1) and B(3,4).
  40. 90.If the tangents drawn at the points O(0,0) and P(1+√5,2) on the circle x^2+y^2-2x-4y=0 int…
  41. 91.If one of the diameters of the circle x^2+y^2-2√2x-6√2y+14=0 is a chord of the circle (x-2…
  42. 92.Let a triangle ABC be inscribed in the circle x^2-√2(x+y)+y^2=0 such that BAC=2.
  43. 93.If the circles x^2+y^2+6x+8y+16=0 and x^2+y^2+2(3-√3)x+2(4-√6)y=k+6√3+8√6, k>0, touch inte…
  44. 94.A circle C_1 passes through the origin O and has diameter 4 on the positive x-axis.
  45. 95.Let C be the centre of the circle x^2+y^2-x+2y=114 and P be a point on the circle.
  46. 96.Let the mirror image of a circle c_1:x^2+y^2-2x-6y+=0 in the line y=x+1 be c_2:5x^2+5y^2+1…
  47. 97.Let P(a,b) be a point on the parabola y^2=8x such that the tangent at P passes through the…
  48. 98.If one of the diameters of the circle x^2+y^2-2x-6y+6=0 is a chord of another circle 'C', …
  49. 99.If the locus of the mid-point of the line segment from the point (3,2) to a point on the c…
  50. 100.Let A(1,4) and B(1,-5) be two points.