Question

The normal to the hyperbola $\frac{ x ^{2}}{ a ^{2}}-\frac{ y ^{2}}{9}=1$ at the point $(8,3 \sqrt{3})$ on it passes through the point :

• A. $(15,-2 \sqrt{3})$
• B. $(9,2 \sqrt{3})$
• C. $(-1,9 \sqrt{3})$
• D. $(-1,6 \sqrt{3})$

Answer 1

Answer: (C)

$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{9}=1 .(8,3 \sqrt{3})$ lie on Hyperbola then $\frac{64}{a^{2}}-\frac{27}{9}=1$
$\Rightarrow a^{2}=\frac{64}{4}=16$
equation of normal at $(8,3 \sqrt{3})$ :
$\frac{16 x}{8}+\frac{9 y}{3 \sqrt{3}}=16+9$
$2 x+\sqrt{3} y=25$