MHT-CET

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Q1.

From point $P(8,27)$ tangents $P Q$ and $P R$ are drawn to the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$. Then, angle subtended by $Q R$ at origin is

(A)

$\tan ^{-1} \frac{2 \sqrt{6}}{65}$

(B)

$\tan ^{-1} \frac{4 \sqrt{6}}{65}$

(C)

$\tan ^{-1} \frac{8 \sqrt{2}}{65}$

(D)

None of these

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Q2.

If $\mathrm{CP}$ and $\mathrm{CD}$ is a pair of semi-conjugate diameters of the ellipse $\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}}=1$, then $\mathrm{CP}^{2}+\mathrm{CD}^{2}=$

(A)

$\frac{a^{2}+b^{2}}{2}$

(B)

$a^{2}+b^{2}$

(C)

$a^{2}-b^{2}$

(D)

$\frac{a^{2}-b^{2}}{2}$

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