Let an ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$ and a parabola $x^{2} = 2 y$ intersecting each other above $X -$ axis at $P$ and $Q$ . Tangents to ellipse at $P and Q$ intersect $Y -$ axis at $R$ and tangents at $P and Q$ drawn to the parabola intersect $Y -$ -axis at $S$ , then which of the following is/are CORRECT?

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area of quadrilateral PRQS is $\frac{15 \sqrt{3}}{2} sq. units$

area of $△ PQR is \frac{9 \sqrt{3}}{2} sq. units$

$\frac{area of △ PQR}{area of △ PQS} = \frac{3}{2}$

area of $△ PQS is \sqrt{3} sq. units$

answer is A, B, C.

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Detailed Solution

POI are $P (\sqrt{3}, \frac{3}{2}), Q (- \sqrt{3}, \frac{3}{2}) and R (0, 6), S (0, - \frac{3}{2})$

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