JEE MATHEMATICS MCQ: HYPERBOLA

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Application +4 | -1

If the tangent at the point

P(a \sec \theta, b \tan \theta)

to the hyperbola

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

passes through the point where a directrix of the hyperbola meets the positive side of the transverse axis, then

\theta

is equal to
Where

e

is the eccentricity of the hyperbola.

View answer and explanation

Correct option: A

\cos ^{-1}(1 / e)

Option A (

\cos^{-1}(1/e)

) is correct because substituting the directrix point into the tangent equation and solving for

\theta

gives

\cos \theta = 1/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

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

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

H

H

e

H

e

\mathrm{H}

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

x - y + 1 = 0

\sqrt 2