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 locus of mid-points of the chords of the circle x^2 - 2x + y^2 - 2y + 1 = 0 which are of unit length is :

The locus of the mid-points of the chords of the circle x^2+ y^2-2x-4y - 11=0 which subtends an angle of 60^@ at center is

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

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 distance of the point (1,-2) from the common chord of the circles x^(2) + y^(2) - 5x +4y - 2= 0 " and " x^(2) +y^(2) - 2x + 8y + 3 = 0

The mid point of the chord x-2y+7=0 w.r.t the circle x^(2)+y^(2)-2x-10y+1=0 is

The minimum length of the chord of the circle x^2+y^2+2x+2y-7=0 which is passing (1,0) 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

The length of the common chord of the circles x^(2)+y^(2)-2x-1=0 and x^(2)+y^(2)+4y-1=0 , is

The point of tangency of the circles x^2+ y^2 - 2x-4y = 0 and x^2 + y^2-8y -4 = 0 , is