Question

Find the length of sub -normal $\frac{x^2}{9}-\frac{y^2}{4}=1$ at $(3,0)$

• A. $\frac{4}{3}$
• B. $\frac{2}{3}$
• C. $\frac{7}{3}$
• D. None of these

Answer 1

The correct option is A $\frac{4}{3}$

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

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

put this in length of sub-normal equation

$=\left|y_1{\left(\frac{4x_1}{9y_1}\right)}_{(3,0)}\right|$

$=\frac{12}{9}=\frac{4}{3}$