Question

Find the length of subnormal to $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at $(3,5)$.

• A. $\frac{25}{9}$
• B. $\frac{9}{25}$
• C. $\frac{5}{3}$
• D. $\frac{3}{5}$

Answer 1

The correct option is A $\frac{25}{9}$

Length of subnormal to $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1at(x_1,y_1)=(1-e^2)x_1$

$=(1-e^2)3$

$b^2=a^2(1-e^2)$

$1-e^2=\frac{b^2}{a^2}$

length of subnormal $=3\frac{b^2}{a^2}$