A tangent is drawn to the ellipse `(x^2)/(27)+y^2=1`at `(3sqrt(3)costh – InterviewSolution

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1.	A tangent is drawn to the ellipse `(x^2)/(27)+y^2=1`at `(3sqrt(3)costheta(0,pi/2)dot`Then findthe value of `theta`such that the sum of intercepts on the axes made by thistangent is minimum.A. `(pi)/(3)`B. `(pi)/(6)`C. `(pi)/(8)`D. `(pi)/(4)`
Answer» Correct Answer - 2 Equation of the tangenth to the ellipese `(x^(2))/(27)+y^(2) =1 at 3sqrt(3 cos theta sin theta),theta in (0,pi//2)` is `(sqrt(3)cos theta)/(9)+y sin theta=1` `therefore` sum of the intercepts =S =`3sqrt(3)theta+cosec theta` For minimum values of s,`(ds)/(d theta)=0` `3(sqrt(3)sin theta)/(cos^(2)theta)-(cos theta)/(sin^(2)theta)=0` or `3sqrt(3)sin^(3) theta - cos^(3) theta =0` or `tan theta =(1)sqrt(3)=tan pi//6 rarr theta -pi//6`

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