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

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

Two tangents OP & OQ are drawn from origin to the circle x^(2)+y^(2)-x+2y+1=0 then the circumcentre of Delta OPQ is

If tangents are drawn from origin to the circle x^(2)+y^(2)-2x-4y+4=0, then

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 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 drawn from the point P(1,8) to the circle x^(2)+y^(2)-6x-4y-11=0 touch the circle at the points A and B. The equation of the circumcircle of the triangle PAB is (A) x^(2)+y^(2)+4x-6y+19=0 (B) x^(2)+y^(2)-4x-10y+19=0 (B) x^(2)+y^(2)-2x+6y-29=0 (D) x^(2)+y^(2)-6x-4y+19=0

If points A and B are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is (a) x^2+y^2=4 (b) x^2+y^2-x-y=0 (c) x^2+y^2-2x-2y+1=0 (d) x^2+y^2+2x-2y+1=0