Question

In ellipse having foci $(3,1),(1,1)$ and passing through the point $(1,3)$ has the eccentricity equals to:

• A. $\sqrt{2}-1$
• B. $\sqrt{2}+1$
• C. $1-\sqrt{2}$
• D. None of these

Answer 1

The correct option is A $\sqrt{2}-1$

$DistanceS1P:d1=\sqrt{{(1-1)}^2+{(3-1)}^2}=2DistanceS2P:d2=\sqrt{{(3-1)}^2+{(1-3)}^2}=2\sqrt{2}DistanceS1S2:D=\sqrt{{(1-3)}^2+{(1-1)}^2}=2$

$Weknow,d1+d2=2a$

$Or,a=\sqrt{2}+1$

$And,D=2ae$

$Or,e=\frac{1}{\sqrt{2}+1}=\sqrt{2}-1$

Option [A]