Question

If $(3,4)$ and $(8,6)$ are the foci of an ellipse passing through the origin, then the eccentricity of the ellipse is

• A. $\frac{\sqrt{29}}{15}$
• B. $\frac{1}{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\sqrt{\frac{15}{29}}$

Answer 1

The correct option is A $\frac{\sqrt{29}}{15}$

If two foci are $S(3,4)$ and $S^{{}^{\prime }}(8,6)$ and the ellipse passes through origin $O$.

Then $SO=\sqrt{9+16}=5,$
$S^{{}^{\prime }}O=\sqrt{64+36}=10$
and $S{S}^{\prime }=\sqrt{29}$

As we know that for an ellipse $SO+S^{{}^{\prime }}O=2a$ and
$S{S}^{{}^{\prime }}=2ae$
$\therefore e=\frac{S{S}^{{}^{\prime }}}{SO+S^{{}^{\prime }}O}=\frac{\sqrt{29}}{15}$