The line x =8 is the directrix of the ellipse | vedclass

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Question

$\frac{ a }{ e }=8 \ldots \ldots \ldots(1) \quad ae =2$

$8 e =\frac{2}{ e }$

$e ^2=\frac{1}{4} \Rightarrow e =\frac{1}{2}$

$a =4$

$b ^2= a

Vedclass · Accepted Answer

$39$

Vedclass · Answer

$\frac{ a }{ e }=8 \ldots \ldots \ldots(1) \quad ae =2$

$8 e =\frac{2}{ e }$

$e ^2=\frac{1}{4} \Rightarrow e =\frac{1}{2}$

$a =4$

$b ^2= a ^2\left(1- e ^2ight)$

$=16\left(\frac{3}{4}ight) \quad=12$

$\frac{ x \cos 	heta}{4}+\frac{ y \sin 	heta}{2 \sqrt{3}}=1$

$\sin 	heta=\frac{1}{2}$

$	heta=30^{\circ}$

$P (2 \sqrt{3}, \sqrt{3})$

$Q \left(\frac{8}{\sqrt{3}}, 0ight)$

$(3 PQ )^2=39$

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