Question

The eccentric angle of the point of contact of the line $\frac{x}{a}+\frac{y}{b}=\sqrt{2}$ with the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, is:

• A. $0$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is C $\frac{\pi }{4}$

At any point ${}^{\prime }{\theta }^{\prime }$ equation of tangent to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is given by,
$\frac{x\cos \theta }{a}+\frac{y\sin \theta }{b}=1$ comparing it with the given line
we get, $\cos \theta =\sin \theta =\frac{1}{\sqrt{2}}\Rightarrow \theta =\frac{\pi }{4}$