Q. If the area of the circle $4x^{2} + 4y^{2} - 8x + 16y + k = 0$ is $9\pi$ sq unit, then the value of $k$ is
A) 4 units
B) 16 units
C) $- 16$ units
D) $\pm 16$ units
Explanation
(c)
Given, $x^{2} + y^{2} - 2x + 4y + \frac{k}{4} = 0$
$\therefore$ Radius of circle $= \sqrt{1 + 4 - \frac{k}{4}}$
Area of circle $= 9\pi$ [given]
$\Rightarrow \ \pi\left( 5 - \frac{k}{4} \right) = 9\pi\ \ \Rightarrow \ k = - 16$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.