The point \( P \) on the ellipse \( 4 x^{2}+9 x^{2}=36 \) is such that the area of the \( \Delta...

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The point \( P \) on the ellipse \( 4 x^{2}+9 x^{2}=36 \) is such that the area of the \( \Delta P F_{1} F_{2}=\sqrt{10} \) where \( F_{1}, F_{2} \) are foci. Then \( P \) has the coordinates
\( \mathrm{P} \)
(a) \( \left(\frac{3}{\sqrt{2}}, \sqrt{2}\right) \)
(b) \( \left(\frac{3}{2}, 2\right) \)
(c) \( \left(-\frac{3}{2},-2\right) \)
(d) \( \left(-\frac{3}{\sqrt{2}},-\sqrt{2}\right) \)
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