EllipseMedium
Question
An ellipse has its center at $(1, - 2)$, one focus at $(3, - 2)$ and one vertex at (5,-2). Then the length of its latus rectum is :
Options
A.$\frac{16}{\sqrt{3}}$
B.6
C.$4\sqrt{3}$
D.$6\sqrt{3}$
Solution
$$\begin{matrix} & {CA}_{1} = a = 4 \\ & {CF}_{1} = ae = 2 \\ & e = \frac{1}{2} \\ & LR = 2e\left( \frac{a}{e} - ae \right) \\ & \ = 2 \times \frac{1}{2} \times \left( \frac{4}{1/2} - 2 \right) \\ & \ = 6 \end{matrix}$$
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