Question

Find the equation of normal to the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$ at the point $(6,\frac{3}{2}\sqrt{5})$

• A. $8\sqrt{5}x+18y=75\sqrt{5}$
• B. $4\sqrt{5}x+9y=25\sqrt{5}$
• C. $4\sqrt{5}x+9y=75\sqrt{5}$
• D. $8\sqrt{5}x+18y=25\sqrt{5}$

Answer 1

Answer: (A)

$8\sqrt{5}x+18y=75\sqrt{5}$

Required normal is given by,
$\frac{a^{2}x}{x_1}+\frac{b^{2}y}{y_1}=a^2+b^2$
$\Rightarrow \frac{16x}{6}+\frac{9y}{\left(3\sqrt{5}/2\right)}=25$
$\Rightarrow 8\sqrt{5}x+18y=75\sqrt{5}$