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Find the length of lactus Rectum for the parabola $y^2=4ax$?

$\begin{array}{1 1}(a)\;4a\\(b)\;2a\\(c)\;3a\\(d)\;8a\end{array}$

1 Answer

The double ordinate passing through the focus is called the latus Rectum of the parabola.
When a line is perpendicular to the axis of parabola and inntersect at two points of the parabola .This two points are known as double ordinate.
Hence here axis is y=0 and latus Rectum is a line perpendicular to the axis and passes through focus hence equation of latus Rectum passing through focus and perpendicular to axis is x=a
Now we know P & Q lie on the parabola & latus Rectum hence for $y^2=4ax$
$\Rightarrow y^2=4a\times a$
$y=\pm 2a$
So $P(a,2a)$ & $Q(a,-2a)$.
Hence length of latus Rectum is 4a
Hence (a) is the correct answer.
answered Feb 6, 2014 by sreemathi.v
edited Sep 28, 2014 by sharmaaparna1

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