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If $P Q$ is a focal chord of the parabola $y^2=4 x$ with focus $S$ and $P=(4,4)$, then $S Q=$
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The correct answer is:
$\frac{5}{4}$
$P Q$ is focal chord of parabola $y^2=4 x$ focus $S(1,0)$ and $P(4,4)$
We know that, Length of Semi-latus rectum is Harmonic mean of $P S$ and $S Q$
$\begin{aligned} \therefore \quad \frac{1}{P S}+\frac{1}{S Q} & =1 \Rightarrow \frac{1}{S Q}=1-\frac{1}{P S} \\ \frac{1}{S Q} & =1-\frac{1}{\sqrt{9+16}}=1-\frac{1}{5}=\frac{4}{5} \Rightarrow S Q=\frac{5}{4}\end{aligned}$
We know that, Length of Semi-latus rectum is Harmonic mean of $P S$ and $S Q$
$\begin{aligned} \therefore \quad \frac{1}{P S}+\frac{1}{S Q} & =1 \Rightarrow \frac{1}{S Q}=1-\frac{1}{P S} \\ \frac{1}{S Q} & =1-\frac{1}{\sqrt{9+16}}=1-\frac{1}{5}=\frac{4}{5} \Rightarrow S Q=\frac{5}{4}\end{aligned}$
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