JEE MATHEMATICS MCQ: HYPERBOLA

1 Easy

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Analyzing +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

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

\mathrm{H}

, then which of the following points lies on the parabola?

View answer and explanation

Correct option: B

(3 \sqrt{3},-6 \sqrt{2})

Option B (

(3 \sqrt{3},-6 \sqrt{2})

) is correct because it satisfies the equation of the parabola

y^2 = 8\sqrt{3}x

after determining the values of a, b, and e.

More Questions from HYPERBOLA

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\phi

\frac{\pi}{2}-\phi

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1

P\left(x_{0}, y_{0}\right)

3 x^{2}-4 y^{2}

=36

3 x+2 y=1

\sqrt{2}\left(y_{0}-x_{0}\right)

x

(2,2)

\frac{1}{2}

9 x^2-16 y^2+72 x-32 y-16=0

\left( {1, - 1} \right),

x - y + 1 = 0

\sqrt 2