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Circle

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  1. 1.Consider the circle C : x^2+y^2-6 x-8 y-11=0
  2. 2.Let the line x-y=4 intersect the circle C:(x-4)^2+(y+3)^2=9 at the points Q and R .
  3. 3.Let the centre of the circle x^2+y^2+2gx+2fy+25=0 be in the first quadrant and lie on the …
  4. 4.Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exa…
  5. 5.If P is a point on the circle x^2+y^2=4, Q is a point on the straight line 5 x+y+2=0 and x…
  6. 6.Let C be the circle x^2+(y-1)^2=2, E_1 and E_2 be two ellipses whose centres lie at the or…
  7. 7.The absolute difference between the squares of the radii of the two circles passing throug…
  8. 8.Let the circle C touch the line x-y+1=0, have the centre on the positive x-axis, and cut o…
  9. 9.Let the centre of a circle, passing through the points (0,0),(1,0) and touching the circle…
  10. 10.Consider two circles C_1:x^2+y^2=25 and C_2:(x- )^2+y^2=16, where (5,9).
  11. 11.Equations of two diameters of a circle are 2 x-3 y=5 and 3 x-4 y=7.
  12. 12.Consider a circle (x- )^2+(y- )^2=50, where , >0.
  13. 13.Two circles in the first quadrant of radii r_1 and r_2 touch the coordinate axes.
  14. 14.Consider a circle C_1:x^2+y^2-4x-2y= -5.
  15. 15.Let the point (p,p+1) lie inside the region E=(x,y):3-x y √9-x^2,0 x 3.
  16. 16.A circle passing through the point P( , ) in the first quadrant touches the two coordinate…
  17. 17.Let P(a_1,b_1) and Q(a_2,b_2) be two distinct points on a circle with center C(√2,√3).
  18. 18.Let C be a circle having centre in the first quadrant and touching the x-axis at a distanc…
  19. 19.Let the point P be the vertex of the parabola y=x^2-6 x+12.
  20. 20.Let P be a moving point on the circle x^2+y^2-6 x-8 y+21=0.
  21. 21.Suppose that two chords, drawn from the point (1,2) on the circle x^2+y^2+x-3 y=0 are bise…
  22. 22.Let a circle pass through the origin and its centre be the point of intersection of two mu…
  23. 23.Let the circle x^2 + y^2 = 4 intersect x-axis at the points A(a, 0), a > 0 and B(b, 0).
  24. 24.Let y=x be the equation of a chord of the circle C_1 (in the closed half-plane x 0 ) of di…
  25. 25.Let a circle of radius 4 pass through the origin O , the points A(-√3a,0) and B(0,-√2b), w…
  26. 26.Let the set of all values of r, for which the circles (x+1)^2+(y+4)^2=r^2 and x^2+y^2-4 x-…
  27. 27.Let PQ and MN be two straight lines touching the circle x^2+y^2-4 x-6 y-3=0 at the points …
  28. 28.Let C_1 be the circle in the third quadrant of radius 3 , that touches both coordinate axe…
  29. 29.If the four distinct points (4,6),(-1,5),(0,0) and (k, 3 k) lie on a circle of radius r, t…
  30. 30.Let a circle C pass through the points (4, 2) and (0, 2), and its centre lie on 3x + 2y + …
  31. 31.Let the line x+y=1 meet the circle x^2+y^2=4 at the points A and B.
  32. 32.Let the equation of the circle, which touches x-axis at the point (a, 0), a>0 and cuts off…
  33. 33.Let circle C be the image of x^2+y^2-2 x+4 y-4=0 in the line 2 x-3 y+5=0 and A be the poin…
  34. 34.A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes.
  35. 35.Let a circle passing through (2,0) have its centre at the point (h,k).
  36. 36.If the image of the point (-4,5) in the line x+2 y=2 lies on the circle (x+4)^2+(y-3)^2=r^…
  37. 37.Let the circles C_1:(x- )^2+(y- )^2=r_2^1 and C_2:(x-8)^2+(y-(15)/(2))^2=r_2^2 touch each …
  38. 38.If P(6,1) be the orthocentre of the triangle whose vertices are A(5,-2),B(8,3) and C(h,k),…
  39. 39.A circle is inscribed in an equilateral triangle of side of length 12.
  40. 40.Let the circle C_1:x^2+y^2-2(x+y)+1=0 and C_2 be a circle having centre at (-1,0) and radi…
  41. 41.Let ABCD and AEFG be squares of side 4 and 2 units, respectively.
  42. 42.Let a circle C of radius 1 and closer to the origin be such that the lines passing through…
  43. 43.Let C be a circle with radius √10 units and centre at the origin.
  44. 44.A square is inscribed in the circle x^2+y^2-10 x-6 y+30=0.
  45. 45.Let the locus of the midpoints of the chords of the circle x^2+(y-1)^2=1 drawn from the or…
  46. 46.Let C:x^2+y^2=4 and C^':x^2+y^2-4 x+9=0 be two circles.
  47. 47.Let a variable line passing through the centre of the circle x^2+y^2-16 x-4 y=0, meet the …
  48. 48.If one of the diameters of the circle x^2+y^2-10 x+4 y+13=0 is a chord of another circle […
  49. 49.If the circles (x+1)^2+(y+2)^2=r^2 and x^2+y^2-4 x-4 y+4=0 intersect at exactly two distin…
  50. 50.Four distinct points (2 k, 3 k),(1,0),(0,1) and (0,0) lie on a circle for k equal to :