A circle `C` and the circle `x^2 + y^2 =1` are orthogonal and have radical axis parallel to y-axis, then `C` can be : (A) `x^2 + y^2 + 1 = 0` (B) `x^2 + y^2 + 1 = y` (C) `x^2 + y^2 + 1 = -x` (D) `x^2 + y^2 - 1 = -x`

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

At what points on the circle x^2+y^2-2x-4y+1=0 , the tangent is parallel to the x-axis.

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

At what point on the circle x^2+y^2-2x-4y+1=0, the tangent is parallel to x-axis.

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 normal at the point (1,1) on the curve 2y+x^2=3 is (A) x + y = 0 (B) x y = 0 (C) x + y +1 = 0 (D) x y = 0

The normal at the point (1,1) on the curve 2y+x^2=3 is (A) x - y = 0 (B) x y = 0 (C) x + y +1 = 0 (D) x y = 0

If the circle x^2+y^2+2a_1x+c=0 lies completely inside the circle x^2+y^2+2a_2x+c=0 then

For the circles 3x^2+3y^2+x+2y-1=0 , 2x^2+2y^2+2x-y-1=0 radical axis is

The circle x^(2) + y^(2) + 2g x + 2fy + c = 0 does not intersect the y-axis if