If a normal to the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) is \( 4 x-3 y=7 \) an....

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If a normal to the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \) is \( 4 x-3 y=7 \)
\( \mathrm{P} \)
and its eccentricity is \( \frac{\sqrt{7}}{4} \), then the value of latus rectum can be
(1) \( \frac{9}{\sqrt{2}} \)
(2) \( \frac{9}{2} \)
(3) \( \frac{8 \sqrt{337}}{19} \)
(4) \( \frac{3 \sqrt{337}}{8} \)


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