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`

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

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 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

The equation of the incircle of the triangle formed by the coordinate axes and the line 4x + 3y - 6 = 0 is (A) x^(2) + y^(2) - 6x - 6y - 9 = 0 (B) 4 (x^(2) + y^(2) - x - y) + 1 = 0 (C) 4 (x^(2) + y^(2) + x + y) + 1 = 0 (D) 4 (x^(2) + y^(2) - x - y ) - 1 = 0

Tangents AB and AC are drawn to the circle x^(2)+y^(2)-2x+4y+1=0 from A(0,1) then equation of circle passing through A,B and C is

The pair of tangents from origin to the circle x^(2)+y^(2)+4x+2y+3=0 is

Find the equation of the common chord of the following pair of circles x^2+y^2+2x+3y+1=0 x^2+y^2+4x+3y+2=0

In triangle A B C , the equation of side B C is x-y=0. The circumcenter and orthocentre of triangle are (2, 3) and (5, 8), respectively. The equation of the circumcirle of the triangle is a) x^2+y^2-4x+6y-27=0 b) x^2+y^2-4x-6y-27=0 c) x^2+y^2+4x-6y-27=0 d) x^2+y^2+4x+6y-27=0

Find the equation of the circle whose diameter is the common chord of the circles x^(2) + y^(2) + 2x + 3y + 1 = 0 and x^(2) + y^(2) + 4x + 3y + 2 = 0

Coordinates of the centre of the circle which bisects the circumferences of the circles x^2 + y^2 = 1; x^2 + y^2 + 2x - 3 = 0 and x^2 + y^2 + 2y-3 = 0 is