EllipseHardBloom L3
Question
An ellipse having foci at $(3,3)$ and $( - 4,4)$ and passing through the origin has eccentricity equal to:
Options
A.$\frac{3}{7}$
B.$\frac{2}{7}$
C.$\frac{5}{7}$
D.$\frac{3}{5}$
Solution
Sol.(c) $PF_{1} + PF_{2} = 2a$
$\Rightarrow 3\sqrt{2} + 4\sqrt{2} = 2a$ [Here $P = (0,0)$ ]
$$\Rightarrow 7\sqrt{2} = 2a$$
$$2ae = \sqrt{7^{2} + 1^{2}} = 5\sqrt{2}$$
$$\Rightarrow \ e = \frac{5\sqrt{2}}{7\sqrt{2}} = \frac{5}{7}$$
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