Question

The least intercept made on the tangents to the ellipse $\frac{x^2}{25}+\frac{y^2}{9}$ = 1 by the axes is

• A. 3
• B. 8
• C. 15
• D. 34

Answer 1

The correct option is A 3

tangent at point $\left(\theta \right)$ to ellipse $:\frac{xcos\theta }{5}+\frac{ysin\theta }{3}=1$

$\frac{x}{5sec\theta }+\frac{y}{3cosec\theta }$ $=1\Rightarrow$ intercepts $5sec\theta$ and $3cosec\theta$

As $sec\theta ,cosec\theta ϵ(-\infty ,-1)\cup (1,\infty )$

$\Rightarrow$ least intercept is when $cosec\theta =$ 1 & is =3