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

Problem: The tangents drawn from the origin $x^2 + y^2 + 2gx + 2fy + f^2 =0$ are perpendicular If

(A) g = f

(B) g = -f

(C) g = 2f

(D) 2g = f

Sol. Since tangents drawn from origin are perpendicular that means origin lies on director circle of given circle.

$\sqrt{g^2 + f^2 } = \sqrt{2}\sqrt{g^2 + f^2 -f^2}$

$\large g^2 + f^2 = 2 g^2$

f = ± g.

Hence (A) and (B) are the correct answer.