Question

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

• A. $g=f$
• B. $g=2f$
• C. $2g=f$
• D. $3g=f$

Answer 1

The correct option is A $g=f$

Since the tangents are parallel, the pair of tangents and radii form a square.

$⟹diagonal=\sqrt{2}\times \text{length of side}$

$⟹CP=\sqrt{2}\times r$

$⟹\sqrt{g^2+f^2}=\sqrt{2}\left(\sqrt{g^2+f^2–f^2}\right)$

$⟹g^2+f^2=2g^2$

$⟹g^2=f^2$

$⟹g=f$