Let \( P \) be a variable point on the ellipse \( \frac{x^{2}}{25}+...

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Let \( P \) be a variable point on the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \)
\( \mathrm{P} \)
W with foci at \( F_{1} \& F_{2} \) :
(1) Maximum area of \( \triangle P F_{1} F_{2} \) is 12
(2) Area of \( \triangle P F_{1} F_{2} \) is maximum when \( P \) is \( (0,2) \)
(3) Co-ordinates of \( P \) is \( (4,0) \)
(4) Centre of the ellipse is \( (1,2) \)
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