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A tangent is drawn to the ellipse (x^2)/...

A tangent is drawn to the ellipse `(x^2)/(27)+y^2=1` at `(3sqrt(3)costheta, sin theta)` where `theta epsilon(0,pi/2)dot` Then find the value of `theta` such that the sum of intercepts on the axes made by this tangent is minimum.

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

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A tangent is drawn at (3sqrt(3) cos theta, sin theta) (0 lt theta lt pi/2) to the ellipse x^(2)/27+y^(2)/1=1 . The value of theta for which the sum of the intercepts on the coordinate axes made by this tangent attains the minimum, is