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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:b

P(θ1),Q(θ2),R(θ3) , P(θ1)=(acosθ1,asinθ1)
Q(θ2)=(acosθ2,asinθ2)
R(θ3)=(acosθ3,asinθ3)
PQR=∣ ∣111acosθ1acosθ2acosθ3bsinθ1bsinθ2bsinθ3∣ ∣
PQR=ab∣ ∣111cosθ1cosθ2cosθ3sinθ1sinθ2sinθ3∣ ∣
PQR=ab∣ ∣111acosθ1acosθ2acosθ3asinθ1asinθ2asinθ3∣ ∣=a2abPQR
PQRPQR=ab

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