Question

If $\frac{x}{a}+\frac{y}{b}=\sqrt{2}$ touches the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at a point $P$, then eccentric angle of $P$ is

• A. $0^o$
• B. ${90}^o$
• C. ${45}^o$
• D. ${60}^o$

Answer 1

The correct option is C ${45}^o$

Equation of tangent in parametric form to an ellipse is

$\frac{x\cos \theta }{a}+\frac{y\sin \theta }{b}=1$

Comparing it with given equation

$\Rightarrow \cos \theta =\frac{1}{\sqrt{2}},\sin \theta =\frac{1}{\sqrt{2}}\Rightarrow \theta =\frac{\pi }{4}$

So the eccentric angle is ${45}^{\circ }$