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 : [2026]

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 : [2026]

Smart Achievers · Accepted Answer

(4)

$C A_{1} = a = 4$

$C F_{1} = a e = 2$

$e = \frac{1}{2}$

$L R = 2 e (\frac{a}{e} - a e)$

$= 2 \times \frac{1}{2} (\frac{4}{1 / 2} - 2)$

$= 6$

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