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Question

P is a variable point on ellipse 9x2+16y2=144 with foci S and S. If K is the area of triangle SSP, then the maximum value of K2 is 


Solution

Equation of the ellipse is
9x2+16y2=144x216+y29=1
a=4,b=3
and e=1916=74
Distance between foci SS=2ae=27
Any point on the ellipse is P(4cosθ,3sinθ)
Area of SSP=12×SS×3sinθ
K=37sinθ
K2=63sin2θ
K2max=63

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