Question

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

• A. $\frac{1}{6}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{1}{3}$

$\mathrm{If}\mathrm{the}\mathrm{foci}\mathrm{be}S(3,4)\mathrm{and}S\text{'}(6,8)\mathrm{and}\mathrm{the}\mathrm{ellipse}\mathrm{passes}\mathrm{through}\mathrm{the}\mathrm{Origin},\mathrm{then},\mathrm{SO}=\sqrt{9+16}=5\mathrm{and}S\text{'}O=\sqrt{36+64}=10\mathrm{and}\mathrm{SS}\text{'}=\sqrt{9+16}=5\mathrm{If}\mathrm{the}\mathrm{conic}\mathrm{is}\mathrm{an}\mathrm{ellipse}\mathrm{then},\mathrm{SO}+S\text{'}O=2a\mathrm{and}\mathrm{SS}\text{'}=2\mathrm{ae}\therefore e=\frac{\mathrm{SS}\text{'}}{\mathrm{SO}+S\text{'}O}=\frac{5}{5+10}=\frac{1}{3}$