An ellipse having foci at (3, 1) and (1, 1) | vedclass

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Question

$S \equiv(3,1), S^{\prime} \equiv(1,1)$ and $P \equiv(1,3)$

$\Rightarrow P S=\sqrt{(3-1)^{2}+(1-3)^{2}}=2 \sqrt{2}, P S^{\prime}=\sqrt{(1-1)^{2}+(1

Vedclass · Accepted Answer

$\sqrt 2  - 1$

Vedclass · Answer

$S \equiv(3,1), S^{\prime} \equiv(1,1)$ and $P \equiv(1,3)$

$\Rightarrow P S=\sqrt{(3-1)^{2}+(1-3)^{2}}=2 \sqrt{2}, P S^{\prime}=\sqrt{(1-1)^{2}+(1-3)^{2}}=2$

Using definition of an ellipse $P S+P S^{\prime}=2 a \Rightarrow a=\sqrt{2}+1$

Also $S S^{\prime}=2 a e=2 \Rightarrow e=\frac{1}{a}=\frac{1}{\sqrt{2}+1}=\sqrt{2}-1$

An ellipse having foci at $(3, 1)$ and $(1, 1) $ passes through the point $(1, 3),$ then its eccentricity is

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