Question

The length of the focal chord of the parabola $y^2=4x$ at a distance of $0.4$ units from the origin is

• A. $22$ units
• B. $23$ units
• C. $24$ units
• D. $25$ units

Answer 1

Answer: (D)

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 $\times {\text{cosec}}^2\theta$
$\Rightarrow PQ=4{\left(2.5\right)}^2=4\times 6.25$
$=25$