The equation of the ellipse referred to its a | vedclass

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Question

$2 \mathrm{ae}=4 \sqrt{2}$      .......$(1)$

$\frac{2 b^{2}}{a}=4$      .....$(2)$

$b^{2}=a^{2}\left(1-e^{2}\right

Vedclass · Accepted Answer

$x^2 + 2y^2 = 16$

Vedclass · Answer

$2 \mathrm{ae}=4 \sqrt{2}$      .......$(1)$

$\frac{2 b^{2}}{a}=4$      .....$(2)$

$b^{2}=a^{2}\left(1-e^{2}\right)$      .....$(3)$

From $(1),(2)$ and $( 3)$

$a=4, b=2 \sqrt{2}$

So, $a^{2}=16, b^{2}=8$

Equation of ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{8}=1$

$\Rightarrow x^{2}+2 y^{2}=16$

The equation of the ellipse referred to its axes as the axes of coordinates with latus rectum of length $4$ and distance between foci $4 \sqrt 2$ is-

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