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(D) For an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ (where $b > a$),the product of the lengths of the perpendiculars from the foci to any tange

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$9$

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(D) For an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ (where $b > a$),the product of the lengths of the perpendiculars from the foci to any tangent is equal to the square of the semi-minor axis,which is $a^2$.Given the equation $\frac{x^2}{9} + \frac{y^2}{25} = 1$,we have $a^2 = 9$ and $b^2 = 25$.Since $b > a$,the semi-minor axis is $a = 3$.The product of the perpendiculars is $a^2 = 9$.

The product of the lengths of the perpendiculars drawn from the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ to the tangent at any point on the ellipse is

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