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Q.
The length of the focal chord of the parabola $y^{2}=4x$ at a distance of $0.4$ units from the origin is
NTA AbhyasNTA Abhyas 2022
Solution:
Let, $PQ$ is a focal chord and $S$ is the focus
Now, $OS=1$
$\Rightarrow $ In $\Delta OSR$ ( $R$ is the foot of the perpendicular from $O$ on $PQ$ )
$\Rightarrow \text{cosec}\theta =\frac{1}{0 . 4}=2.5$
Length of $PQ=$ length of latus rectum $\times \text{cosec}^{2}\theta $
$\Rightarrow PQ=4\left(2 .5\right)^{2}=4\times 6.25$
$=25$
