Question

Find the equation of normal to the hyperbola $\frac{x^2}{36}-\frac{y^2}{9}=1$ at point $(10,4).$

• A. $8x+5y=100$
• B. $5x-8y=100$
• C. $8x-5y=100$
• D. $5x+8y=100$

Answer 1

The correct option is A $8x+5y=100$

Given: Hyperbola $\frac{x^2}{36}-\frac{y^2}{9}=1$; Point $(10,4)$

To Find: Equation of normal

$\Rightarrow \frac{x^2}{36}-\frac{y^2}{9}=1$

Hence, $a=6,b=3$

and $(x_1,y_1)=(10,4)$

Equation of normal in point form is: $\frac{a^{2}x}{x_1}+\frac{b^{2}y}{y_1}=a^2+b^2$

$\therefore$ Equation of normal is
$\frac{36x}{10}+\frac{9y}{4}=36+9$

$\Rightarrow \frac{72x+45y}{20}=45$

$\Rightarrow 72x+45y=900$

$\Rightarrow 8x+5y=100$