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If a normal to the ellipse (x^(2))/(a^(...

If a normal to the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` u=is `4-3y=7` and its ecentricity is `(sqrt(7))/(4)` , then the volume of L.R can be

A

`(9)/(sqrt(2))`

B

`(9)/(2)`

C

`(8sqrt(337))/(19)`

D

`(3sqrt(337))/(8)`

Text Solution

AI Generated Solution

To solve the problem step by step, we will follow the reasoning provided in the video transcript and derive the necessary equations to find the volume of the lattice rectum (L.R) of the ellipse. ### Step 1: Understand the ellipse and the normal equation The equation of the ellipse is given as: \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \] The normal to the ellipse at the point \((a \cos \theta, b \sin \theta)\) is given by: ...
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