First slide

Ellipse

Question

$An ellipse having foci at (3, 3) and (1,4) and passing through the origin has eccentricity equal to$

Moderate

A

$\frac{3}{5}$
B

$\frac{2}{5}$
C

$\frac{5}{7}$
D

$\frac{3}{7}$

Solution

$The ellipse is passing through O(0, 0) and has foci P(3,3) and Q(4,4). Then,$
$e = \frac{P Q}{O P + O Q} = \frac{\sqrt{50}}{3 \sqrt{2} + 4 \sqrt{2}} = \frac{5}{7}$

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