Q. The equation of the director circle of the hyperbola $9x^{2} - 16y^{2} = 144$ is
A) $x^{2} + y^{2} = 7$
B) $x^{2} + y^{2} = 9$
C) $x^{2} + y^{2} = 16$
D) $x^{2} + y^{2} = 25$
Explanation
(a)
Given equation can be rewritten as
$\frac{x^{2}}{16}\ –\frac{y^{2}}{9}\ = 1$
$\therefore$ Required equation of director circle is
$x^{2} + y^{2} = 16 - 9$
$\Rightarrow \ x^{2} + y^{2} = 7\$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.