JEE MATHEMATICS MCQ: HYPERBOLA

1 Hard

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Analyzing +4 | -1

Let

F_1, F_2

are the foci of the hyperbola

\frac{x^2}{16}-\frac{y^2}{9}=1

and

F_3, F_4

are the foci of its conjugate hyperbola. If

\mathrm{e}_{\mathrm{H}}

and

\mathrm{e}_{\mathrm{C}}

are eccentricities of hyperbola and its conjugate hyperbola respectively, then the statement which holds TRUE is :

View answer and explanation

Correct option: C

Area of the quadrilateral formed by their foci is 50 sq. units.

Option C (Area of the quadrilateral formed by their foci is 50 sq. units) is correct because the area of the quadrilateral formed by the foci of the hyperbola and its conjugate is indeed 50 square units.

More Questions from HYPERBOLA

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Locus of the point of intersection of the tangents at the points with eccentric angles

\phi

and

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

on the hyperbola

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

is Let

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

be the point on the hyperbola

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

=36

, which is nearest to the line

3 x+2 y=1

. Then

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

is equal to Suppose an ellipse and a hyperbola have the same pair of foci on the

x

-axis with centres at the origin and they intersect at

(2,2)

. If the eccentricity of the ellipse is

\frac{1}{2}

, then the eccentricity of the hyperbola, is The eccentricity of the hyperbola

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

, is 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? The equation of the conic with focus at

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

directrix along

x - y + 1 = 0

and with eccentricity

\sqrt 2