Let the tangent at A(p,q) to the ellipse x216+y24=1 form a triangle of least area with the coordinate axes (p,q>0) . Then p2+q2 is equal to

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answer is 10.

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Detailed Solution

T:x4cos⁡θ+y2sin⁡θ=1 Area =12(4sec⁡θ)(2cosec⁡θ) Area =8sin⁡2θ For area to be least θ=π4 . ∴p=22 and q=2∴p2+q2=8+2=10

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