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Question

Let P,Q,R be three points on the ellipse x2a2+y2b2=1 and P′,Q′ and R′ be the corresponding points on the auxiliary circle. Then,Area of ΔPQR : Area of Δ P' Q' R' =

A
a:b
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B
b:a
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C
a2:b2
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D
b2:a2
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Solution

The correct option is A a:bP(θ1),Q(θ2),R(θ3) , P′(θ1)=(acosθ1,asinθ1)Q′(θ2)=(acosθ2,asinθ2)R′(θ3)=(acosθ3,asinθ3)△PQR=∣∣ ∣∣111acosθ1acosθ2acosθ3bsinθ1bsinθ2bsinθ3∣∣ ∣∣△PQR=ab∣∣ ∣∣111cosθ1cosθ2cosθ3sinθ1sinθ2sinθ3∣∣ ∣∣△P′Q′R′=ab∣∣ ∣∣111acosθ1acosθ2acosθ3asinθ1asinθ2asinθ3∣∣ ∣∣=a2ab△PQR△P′Q′R△PQR=ab

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