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Let $L L^{\prime}$ be the latus rectum and PQ be the focal chord of the parabola $y^2=16 x$. If $\mathrm{P}=(1,4)$ and $\mathrm{P}, \mathrm{L}$ lie in the same quadrant then $\mathrm{LQ}=$
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Verified Answer
The correct answer is:
$12 \sqrt{5}$
Acc. to question, given parabola is.
$$
\begin{aligned}
& \mathrm{y}^2=16 \mathrm{x} \Rightarrow \mathrm{a}=4 \\
& \because \mathrm{P}=(1,4) \Rightarrow \mathrm{Q}=(16,-16) \text { and } \mathrm{L}=(4,8) \\
& \text { Now } \mathrm{LQ}=\sqrt{12^2+24^2}=12 \sqrt{5}
\end{aligned}
$$
$$
\begin{aligned}
& \mathrm{y}^2=16 \mathrm{x} \Rightarrow \mathrm{a}=4 \\
& \because \mathrm{P}=(1,4) \Rightarrow \mathrm{Q}=(16,-16) \text { and } \mathrm{L}=(4,8) \\
& \text { Now } \mathrm{LQ}=\sqrt{12^2+24^2}=12 \sqrt{5}
\end{aligned}
$$
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