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If $\mathrm{P}\left(\frac{1}{2}, 4\right)$ and $\mathrm{Q}$ are the ends of a focal chord of the parabola $y^2=32 x$ and $\mathrm{S}$ is the focus of the parabola then $\mathrm{SQ}=$
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The correct answer is:
136
Given parabola $y^2=32 x$
$$
\begin{aligned}
& \Rightarrow \mathrm{a}=8, \mathrm{~S}=(8,0) \\
& \text { and } \mathrm{P}=\left(\frac{1}{2}, 4\right) \Rightarrow \mathrm{Q}=(128,-64) \\
& \text { Now } \mathrm{SQ}=\sqrt{(128-8)^2+(-64)^2}=136
\end{aligned}
$$
$$
\begin{aligned}
& \Rightarrow \mathrm{a}=8, \mathrm{~S}=(8,0) \\
& \text { and } \mathrm{P}=\left(\frac{1}{2}, 4\right) \Rightarrow \mathrm{Q}=(128,-64) \\
& \text { Now } \mathrm{SQ}=\sqrt{(128-8)^2+(-64)^2}=136
\end{aligned}
$$
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