Q. The equation of the tangent to the circle $x^{2} + y^{2} + 4x - 4y + 4 = 0$ which makes equal intercepts on the positive coordinate axes, is
A) $x + y = 2$
B) $x + y = 2\sqrt{2}$
C) $x + y = 4$
D) $x + y = 8$
Explanation
(b)
Let the equations of the required tangent be $x + y = a$, then length of the perpendicular from centre=radius
$\therefore\ \ \ \left| \frac{- 2 + 2 - a}{\sqrt{a}} \right| = 2\ \ \Rightarrow \ \ a = 2\sqrt{2}$
Hence, the equation of tangent is
$x + y = 2\sqrt{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.