Question

The area of the rectangle formed by the perpendicular from centre of $\frac{x^2}{9}+\frac{y^2}{4}=1$, to the tangent and the normal at the point whose eccentric angle is $\frac{\pi }{4}$ equals

• A. $\frac{30}{13}$
• B. $\frac{30}{11}$
• C. $\frac{13}{30}$
• D. $\frac{26}{11}$

Answer 1

The correct option is A $\frac{30}{13}$

We use the formula

$\frac{(a^2-b^2)ab}{a^2+b^2}$

$\frac{x^2}{9}+\frac{y^2}{4}=1$

$\Rightarrow a^2=9,b^2=4$

$\therefore \frac{(a^2-b^2)ab}{a^2+b^2}=\frac{(9-4)\left(9\right)\left(4\right)}{9+4}$

$\frac{5\times 3\times 2}{13}$

$\frac{30}{13}$