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(D) The equation of the ellipse is $\frac{x^2}{16} + \frac{y^2}{9} = 1$,where $a^2 = 16$ and $b^2 = 9$.The director circle of an ellipse $\frac{x^2}{a

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$\frac{\pi}{2}$

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(D) The equation of the ellipse is $\frac{x^2}{16} + \frac{y^2}{9} = 1$,where $a^2 = 16$ and $b^2 = 9$.The director circle of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is given by $x^2 + y^2 = a^2 + b^2$.Here,$a^2 + b^2 = 16 + 9 = 25$.Thus,the given circle $x^2 + y^2 = 25$ is the director circle of the ellipse.By definition,the locus of the point of intersection of perpendicular tangents to an ellipse is its director circle.Therefore,the angle between the tangents drawn from any point on the director circle to the ellipse is $\frac{\pi}{2}$.

If tangents are drawn from any point on the circle $x^2+y^2=25$ to the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$,then the angle between the tangents is

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