First slide

Ellipse

Question

An ellipse passing through the origin has its foci at (3,4) and (6,8), and length of its semi-minor axis L. The value of $\frac{L}{\sqrt{2}}$ is

Easy

Solution

$P S^{'} + P S = 2 a 2a=5+10=15 a= \frac{15}{2} 2 a e = \sqrt{{(6 - 3)}^{2} + {(8 - 4)}^{2}} = 5 e = \frac{1}{3} ∴ b^{2} = \frac{225}{4} (1 - \frac{1}{9}) = 50 b = 5 \sqrt{2} = L \frac{L}{\sqrt{2}} = 5$

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