Question

Find the length of sub -normal of $\frac{x^2}{4}-\frac{y^2}{9}=1$ at $(2,0)$.

• A. $\frac{9}{2}$
• B. 3
• C. $\frac{19}{2}$
• D. None of these

Answer 1

The correct option is A $\frac{9}{2}$

Length of sub-normal
$=\left|y_1{\left(\frac{dy}{dx}\right)}_{(x_1,y_1)}\right|$

$\frac{dy}{dx}=\frac{9x}{4y}$

put this in length of sub-normal equation

$=\left|y_1{\left(\frac{9x_1}{4y_1}\right)}_{(2,0)}\right|$

$=\frac{18}{4}=\frac{9}{2}$