C is the centre of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ and
L is an end of a latusrectum. If the normal at
L meets the major axis at G then CG =

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2 ${ae}^{2}$ ae

${ae}^{3}$

$a^{2} e^{2}$

answer is C.

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Detailed Solution

$L (ae, \frac{b^{2}}{a}) normal at L is \frac{a^{2} x}{ae} - \frac{b^{2} y}{\frac{b^{2}}{a}} = a^{2} - b^{2} \frac{ax}{e} - ay = a^{2} e^{2} it meet s x - a xis a t G put y = 0 t h e n x = {ae}^{3} ∴ G ({ae}^{3}, 0) CG = {ae}^{3}$

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