If the angle between the tangents drawn to `x^2+y^2+2gx+2fy+c=0` from (0, 0) is `pi/2,` then
(a) `g^2+f^2=3c` (b) `g^2+f^2=2c` (c) `g^2+f^2=5c` (d) `g^2+f^2=4c`

The tangents drawn from the origin x^2+y^2+2gx+2fy+f^2=0 are perpendicular if

The angle between the tangents to the curve y=x^2-5x+6 at the point (2, 0) and (3, 0) is (a) pi/2 (b) pi/3 (c) pi (d) pi/4

The squared length of the intercept made by the line x=h on the pair of tangents drawn from the origin to the circle x^2+y^2+2gx+2fy+c=0 is (a) (4c h^2)/((g^2-c)^2)(g^2+f^2-c) (b) (4c h^2)/((f^2-c)^2)(g^2+f^2-c) (c) (4c h^2)/((f^2-f^2)^2)(g^2+f^2-c) (d) none of these

The distance between the chords of contact of the tangent to the circle x^2+y^2+2gx+2fy+c=0 from the origin and the point (g, f) is

Find the length of the tangent drawn from any point on the circle x^2+y^2+2gx+2fy+c_1=0 to the circle x^2+y^2+2gx+2fy+c_2=0

The equation x^(2) + y^(2) + 2gx + 2fy + c = 0 represents a point-circle when -

Find the area of an equilateral triangle inscribed in the circle x^2 + y^2 + 2gx + 2fy + c = 0

The length of the tangent drawn from any point on the circle x ^(2) +y^(2) +2gx+2fy+c_(1) =0 to the circel x ^(2)+y^(2) +2gx+2fy+c_(2) =0 is-

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

Find the area of the equilateral triangle inscribed in the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 .