Ellipse

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Question

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

Moderate

Solution

$\begin{array}{l} 2 a = 5 + 10 = 15 \\ a = \frac{15}{2} \\ 2 a e = \sqrt{(6 - 3)^{2} + (8 - 4)^{2}} = 5 \\ e = \frac{1}{3} \\ ∴ b^{2} = \frac{225}{4} (1 - \frac{1}{9}) = 50 \end{array}$

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