# The radius of the director circle of the conic $9x^{2}+16y^{2}=144$ is

$\begin{array}{1 1}(1)\sqrt{7}&(2)4\\(3)3&(4)5\end{array}$

$9x^2+16y^2=144$
$\large\frac{9x^2}{144} +\frac{16y^2}{144} $$=1 \large\frac{x^2}{16} +\frac{y^2}{9}$$=1$
$a^2= 16$
$b^2=9$
Radius of the director circle is
$\qquad= \sqrt {a^2+b^2}$
$\qquad= \sqrt {16+9}$
$\qquad= \sqrt {25}$
$\qquad=5$
Hence 4 is the correct answer