Question

An ellipse having foci at $(3,3)$ and $(-4,4)$ and passing through the origin has eccentricity equal to:

• A. $\frac{3}{7}$
• B. $\frac{2}{7}$
• C. $\frac{5}{7}$
• D. $\frac{3}{5}$

Answer 1

The correct option is C $\frac{5}{7}$

Here $P{S}_1+P{S}_2=2a$

$P{S}_1=\sqrt{3^2+3^2}=3\sqrt{2}$

$P{S}_2=\sqrt{4^2+4^2}=4\sqrt{2}$

$\Rightarrow P{S}_1+P{S}_2=2a=7\sqrt{2}$

Also $2ae=S_1{S}_2=\sqrt{1+49}=5\sqrt{2}$

Thus, $\frac{2ae}{2a}=\frac{5\sqrt{2}}{7\sqrt{2}}=\frac{5}{7}=e$

Thus, eccentricity $e=\frac{5}{7}$