TS EAMCET · Maths · Parabola
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 \(\mathrm{LQ}=\)
- A 5
- B 20
- C \(24 \sqrt{5}\)
- D \(12 \sqrt{5}\)
Answer & Solution
Correct Answer
(D) \(12 \sqrt{5}\)
Step-by-step Solution
Detailed explanation
Acc. to question, given parabola is. \[ \begin{aligned} & \mathrm{y}^2=16 \mathrm{x} \Rightarrow \mathrm{a}=4 \\ & \because \mathrm{P}=(1,4) \Rightarrow \mathrm{Q}=(16,-16) \text { and } \mathrm{L}=(4,8) \\ & \text { Now } \mathrm{LQ}=\sqrt{12^2+24^2}=12 \sqrt{5} \end{aligned} \]
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