Identify the statements which are True.

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(D) Statement $A$: The ellipse is $\frac{x^2}{9} + \frac{y^2}{5} = 1$. Here $a^2 = 9$ and $b^2 = 5$. The director circle is $x^2 + y^2 = a^2 + b^2 = 9

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All of the above.

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(D) Statement $A$: The ellipse is $\frac{x^2}{9} + \frac{y^2}{5} = 1$. Here $a^2 = 9$ and $b^2 = 5$. The director circle is $x^2 + y^2 = a^2 + b^2 = 9 + 5 = 14$. This is true.Statement $B$: The coordinates of $P$ and $Q$ are $(a \cos 	heta, b \sin 	heta)$ and $(a \cos(	heta + \alpha), b \sin(	heta + \alpha))$. The area of $	riangle OPQ$ is $\frac{1}{2} |x_P y_Q - x_Q y_P| = \frac{1}{2} |ab \cos 	heta \sin(	heta + \alpha) - ab \cos(	heta + \alpha) \sin 	heta| = \frac{1}{2} ab |\sin(	heta + \alpha - 	heta)| = \frac{1}{2} ab |\sin \alpha|$. This is independent of $	heta$. This is true.Statement $C$: This is a standard property of parabolas. The locus of the foot of the perpendicular from the focus to any tangent is the tangent at the vertex. This is true.Since all statements are true,the correct option is $D$.

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