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Find the length of lactus rectum and end points of lactus rectum for a ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$?

$\begin{array}{1 1}(a)\;\large\frac{2b^2}{a}\\(b)\;\large\frac{b^2}{a}\\(c)\;\large\frac{4b^2}{a}\\(d)\;\large\frac{2a^2}{b}\end{array}$

1 Answer

Latus rectum is a perpendicular line passing through focus hence let the end points be $L(ae,k)$ & $L'(ae,-k)$.
Length of latus rectum LL'=$2k$
$2k=\large\frac{2b^2}{a}=$$LL'$(length of lactus rectum)
Hence (a) is the correct answer.
answered Feb 7, 2014 by sreemathi.v
edited Sep 28, 2014 by sharmaaparna1

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