If tangents \( P Q \) and \( P R \) are drawn from a point on the circle \( x^{2}+y^{2}=25 \) to...

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If tangents \( P Q \) and \( P R \) are drawn from a point on the circle \( x^{2}+y^{2}=25 \) to the ellipse \( \frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1,(b4) \),
\( \mathrm{P} \) so that the fourth vertex \( S \) of parallelogram \( P Q S R \) lies on the circumcircle of triangle \( P Q R \), then the eccentricity of the ellipse is
(a) \( \frac{\sqrt{5}}{4} \)
(b) \( \frac{\sqrt{5}}{3} \)
(c) \( \frac{\sqrt{7}}{4} \)
(d) \( \frac{\sqrt{7}}{3} \)
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