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Question

Let S and S1 be the foci of the ellipse 9x2+5y2=30y and a point P be (3, 3). The area of triangle PSS1 is


Solution

Given ellipse, 9x2+5y2=30y can be written as
9x2+5(y26y)=0
=9x2+5(y3)2=45
=x25+(y3)291
Centre is (0, 3)
Foci are S(0, 3+95), S1(0, 395)
S(0, 5), S1(0, 1)
Area of ΔPSS1=12∣ ∣331051011∣ ∣=122=6

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