JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let the hyperbola \(H : \frac{ x ^{2}}{ a ^{2}}-\frac{ y ^{2}}{ b ^{2}}=1\) pass through the point \((2 \sqrt{2},-2 \sqrt{2})\). A parabola is drawn whose focus is same as the focus of \(H\) with positive abscissa and the directrix of the parabola passes through the other focus of \(H\). If the length of the latus rectum of the parabola is e times the length of the latus rectum of \(H\), where \(e\) is the eccentricity of \(H\), then which of the following points lies on the parabola?
- A \((2 \sqrt{3}, 3 \sqrt{2})\)
- B \((3 \sqrt{3},-6 \sqrt{2})\)
- C \((\sqrt{3},-\sqrt{6})\)
- D \((3 \sqrt{6}, 6 \sqrt{2})\)
Answer & Solution
Correct Answer
(B) \((3 \sqrt{3},-6 \sqrt{2})\)
Step-by-step Solution
Detailed explanation
\(H: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) Foci : S (ae, 0), S' \((- ae , 0)\) Foot of directrix of parabola is \((- ae , 0)\) Focus of parabola is (ae, 0 ) Now, semi latus rectum of parabola \(=\left| SS ^{\prime}\right|=2 ae\) Given,…
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