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(D) The given circle is $x^2+y^2=25$,which is the director circle of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ because the radius of the director c

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$\frac{\pi}{2}$

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(D) The given circle is $x^2+y^2=25$,which is the director circle of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ because the radius of the director circle is $\sqrt{a^2+b^2} = \sqrt{16+9} = \sqrt{25} = 5$.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 $90^\circ$ or $\frac{\pi}{2}$ radians.

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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