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Hyperbola question

2022 · 28 Jul · Shift 2 · Q32

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JEE Main
Mathematics
Hyperbola
2022 · 28 Jul · Shift 2 · Q32

Hyperbola question

2022 · 28 Jul · Shift 2 · Q32

JEE MainMathematicsHyperbolaMCQ+4 / −1

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

\mathrm{H}

with positive abscissa and the directrix of the parabola passes through the other focus of

\mathrm{H}

. If the length of the latus rectum of the parabola is e times the length of the latus rectum of

\mathrm{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
$\mathbf(3 \sqrt{3},-6 \sqrt{2})$
C
$(\sqrt{3},-\sqrt{6})$
D
$(3 \sqrt{6}, 6 \sqrt{2})$

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