JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The line \(x =8\) is the directrix of the ellipse \(E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) with the corresponding focus \((2,0)\). If the tangent to \(E\) at the point \(P\) in the first quadrant passes through the point \((0,4 \sqrt{3})\) and intersects the \(x\)-axis at \(Q\), then \((3PQ)^2\) is equal to \(........\)
- A \(38\)
- B \(39\)
- C \(35\)
- D \(36\)
Answer & Solution
Correct Answer
(B) \(39\)
Step-by-step Solution
Detailed explanation
\(\frac{ a }{ e }=8 \ldots \ldots \ldots(1) \quad ae =2\) \(8 e =\frac{2}{ e }\) \(e ^2=\frac{1}{4} \Rightarrow e =\frac{1}{2}\) \(a =4\) \(b ^2= a ^2\left(1- e ^2\right)\) \(=16\left(\frac{3}{4}\right) \quad=12\) \(\frac{ x \cos \theta}{4}+\frac{ y \sin \theta}{2 \sqrt{3}}=1\)…
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