JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Consider the parabola with vertex \(\left(\frac{1}{2}, \frac{3}{4}\right)\) and the directrix \(\mathrm{y}=\frac{1}{2}\). Let \(\mathrm{P}\) be the point where the parabola meets the line \(\mathrm{x}=-\frac{1}{2}\). If the normal to the parabola at \(\mathrm{P}\) intersects the parabola again at the point \(\mathrm{Q}\), then \((\mathrm{PQ})^{2}\) is equal to :
- A \(\frac{75}{8}\)
- B \(\frac{125}{16}\)
- C \(\frac{25}{2}\)
- D \(\frac{15}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{125}{16}\)
Step-by-step Solution
Detailed explanation
\(\left(y-\frac{3}{4}\right)=\left(x-\frac{1}{2}\right)^{2} \ldots(1)\) For \(x=-\frac{1}{2}\) \(y-\frac{3}{4}=1 \Rightarrow y=\frac{7}{4} \Rightarrow P\left(-\frac{1}{2}, \frac{7}{4}\right)\) Now \(\mathrm{y}^{\prime}=2\left(\mathrm{x}-\frac{1}{2}\right) \quad\) At…
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