Q. The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the $x$ and $y$-axes respectively are
A) $x^{2} + y^{2} \pm 4x \pm 8y = 0$
B) $x^{2} + y^{2} \pm 2x \pm 4y = 0$
C) $x^{2} + y^{2} \pm 8x \pm 16y = 0$
D) $x^{2} + y^{2} \pm x \pm y = 0$
Explanation
(a)
In $\mathrm{\Delta}OAC,\ OC^{2} = 2^{2} + 4^{2} = 20$
[image:11_image24.emf]
$\therefore$ Required equation of circle is
$(x \pm 2)^{2} + (y \pm 4)^{2} = 20$
$\Rightarrow x^{2} + y^{2} \pm 4x \pm 8y = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.