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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 2020Conic Sections
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 $PQ$ )
$\Rightarrow cosec\theta =\frac{1}{0 . 4}=2.5$
Length of $PQ$ is equal to the length of latus rectum $\times cosec^{2}\theta $
$\Rightarrow PQ=4\left(2.5\right)^{2}=4\times 6.25$
$=25$
