Question

An ellipse passing through origin has its foci at $(5,12)$ and $(24,7)$, then its eccentricity is

• A. $\frac{\sqrt{386}}{38}$
• B. $\frac{\sqrt{386}}{39}$
• C. $\frac{\sqrt{386}}{47}$
• D. $\frac{\sqrt{386}}{51}$

Answer 1

Answer: (A)

$\frac{\sqrt{386}}{38}$

$SP+S{P}^{\prime }=2a=\sqrt{(5{)}^2+(12{)}^2}+\sqrt{(24{)}^2+(7{)}^2}$
$=13+25$
$=38$
$2ae=\sqrt{(24-5{)}^2+(12-7{)}^2}$
$=\sqrt{386}$
$e=\frac{\sqrt{386}}{38}$