Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$S=(5,12)S^{\prime }=(24,7)\overline{S{S}^{\prime }}=2ae=\sqrt{386}$
also $SP+S^{\prime }P=2a$
Here P=(0,0)
$\therefore 13+25=2a\Rightarrow 2a=38\therefore e=\frac{\sqrt{386}}{2a}=\frac{\sqrt{386}}{38}$