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Q.

Let a tangent be drawn to the ellipse x227+y2=1 at (33cosθ,sinθ) where θ∈0,π2 . Then the value of θ such that the sum of intercepts on axes made by this tangent is minimum is equal to :

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a

π3

b

π6

c

π4

d

π8

answer is B.

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Detailed Solution

equation of tangent is (cosθ)x33+(sinθ)y=1 Sum of intercepts =33secθ+cosecθ=f(θ) For minima, f'(θ)=0⇒33secθtanθ-cosecθcotθ=033secθtanθ=cscθcotθ33sinθcos2θ=cosθsin2θtan3θ=33tanθ=3θ=π3
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