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JEE MATHEMATICS MCQ: HYPERBOLA

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The normal at

P\left(x_1, y_1\right)

on the hyperbola

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

meets the coordinate axes at

A

and

B

. If

O

, is the origin and

e

, the eccentricity of the hyperbola, then

View answer and explanation

Correct option: A

O A=e^2 x_1

Option A (

OA=e^2 x_1

) is correct because the x-intercept of the normal is

e^2x_1

, which represents the distance OA.

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

\phi

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

on the hyperbola

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

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

\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

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