The equation of the circle passing through (1, 0) and (0, 1) and having smallest possible radius is : (A) `2x^2 + y^2 - 2x-y=0` (B) `x^2 + 2y^2 - x - 2y = 0` (C) `x^2 = y^2 - x - y = 0` (D) `x^2 + y^2 + x + y = 0`

The equation of the circle passing through (1/2, -1) and having pair of straight lines x^2 - y^2 + 3x + y + 2 = 0 as its two diameters is : (A) 4x^2 + 4y^2 + 12x - 4y - 15 = 0 (B) 4x^2 + 4y^2 + 15x + 4y - 12 = 0 (C) 4x^2 + 4y^2 - 4x + 8y + 5 = 0 (D) none of these

The circles x^2 + y^2 + 6x + 6y = 0 and x^2 + y^2 - 12x - 12y = 0

The locus of the mid-point of a chord of the circle x^2 + y^2 -2x - 2y - 23=0 , of length 8 units is : (A) x^2 + y^2 - x - y + 1 =0 (B) x^2 + y^2 - 2x - 2y - 7 = 0 (C) x^2 + y^2 - 2x - 2y + 1 = 0 (D) x^2 + y^2 + 2x + 2y + 5 = 0

Tangents OA and OB are drawn from the origin to the circle (x-1)^2 + (y-1)^2 = 1 . Then the equation of the circumcircle of the triangle OAB is : (A) x^2 + y^2 + 2x + 2y = 0 (B) x^2 + y^2 + x + y = 0 (C) x^2 + y^2 - x - y = 0 (D) x^2+ y^2 - 2x - 2y = 0

The equation of the circle passing through (1,2) and the points of intersection of the circles x^2+y^2-8x-6y+21=0 and x^2+y^2-2x-15=0 is

Three sides of a triangle are represented by lines whose combined equation is (2x+y-4) (xy-4x-2y+8) = 0 , then the equation of its circumcircle will be : (A) x^2 + y^2 - 2x - 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 2x + 4y = 0 (D) x^2 + y^2 + 2x - 4y = 0

Let P be the point on the parabola, y^2=8x which is at a minimum distance from the centre C of the circle, x^2+(y+6)^2=1. Then the equation of the circle, passing through C and having its centre at P is : (1) x^2+y^2-4x+8y+12=0 (2) x^2+y^2-x+4y-12=0 (3) x^2+y^2-x/4+2y-24=0 (4) x^2+y^2-4x+9y+18=0

The equation of the circle having the intercept on the line y+2x=0 by the circle x^2 + y^2 + 4x + 6y = 0 as a diameter is : (A) 5x^2 + 5y^2 - 8x + 16y =0 (B) 5x^2 + 5y^2 + 8x - 16y =0 (C) 5x^2 + 5y^2 - 8x - 16y =0 (D) 5x^2 + 5y^2 + 8x+- 16y =0

The equation of the circle passing through the point (1,1) and having two diameters along the pair of lines x^2-y^2-2x+4y-3=0 is a. x^2+y^2-2x-4y+4=0 b. x^2+y^2+2x+4y-4=0 c. x^2+y^2-2x+4y+4=0 d. none of these

The equation of the circle passing through the foci of the ellipse (x^2)/(16)+(y^2)/9=1 , and having centre at (0, 3) is (1) x^2+y^2-6y+7=0 (2) x^2+y^2-6y-5=0 (3) x^2+y^2-6y+5=0 (4) x^2+y^2-6y-7=0