If $\left( \sqrt{3} \right)bx + ay = 2ab$ touches the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$, then eccentric angle $\phi$ is

Question

Dr. Abubacker · Accepted Answer

(a)
Given equation of tangent is $\frac{x}{a}\frac{\sqrt{3}}{2} + \frac{y}{b}\frac{1}{2} = 1$ and equation of tangent at the point $\left( a\cos\phi,\ b\sin\phi ight)$ on the ellipse is $\frac{x}{a}\cos\phi + \frac{y}{b}\sin\phi = 1$
Both are same
$	herefore\cos\phi = \frac{\sqrt{3}}{2},\ \sin\phi = \frac{1}{2} \Rightarrow \phi = \frac{\pi}{6}$

Q. If $\left( \sqrt{3} \right)bx + ay = 2ab$ touches the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$, then eccentric angle $\phi$ is

Explanation

Reviewed by Dr. Abubacker

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