Tangent is drawn to ellipse frac{{{x^2}}}{{27 | vedclass

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Question

$\frac{x \cos 	heta}{3 \sqrt{3}}+y \sin 	heta=1.$

Sum of intercepts $ = 3\sqrt 3 \sec 	heta  + \cos ec	heta  = {m{f}}(	heta )$ say

Vedclass · Accepted Answer

$\pi /6$

Vedclass · Answer

$\frac{x \cos 	heta}{3 \sqrt{3}}+y \sin 	heta=1.$

Sum of intercepts $ = 3\sqrt 3 \sec 	heta  + \cos ec	heta  = {m{f}}(	heta )$ say

$f'\,(	heta ) = \frac{{3\sqrt 3 {{\sin }^3}	heta  - {{\cos }^3}	heta }}{{{{\sin }^2}	heta {{\cos }^2}	heta }}$

At $	heta=\frac{\pi}{6}, f(	heta)$ is minimum

Tangent is drawn to ellipse $\frac{{{x^2}}}{{27}} + {y^2} = 1\,at\,(3\sqrt 3 \cos \theta ,\sin \theta )$ where $\theta \in (0, \pi /2)$ . Then the value of $\theta$ such that sum of intercepts on axes made by this tangent is minimum, is

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