List of top Mathematics Questions on Hyperbola asked in AP EAMCET

If the eccentricity of the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) is \( \sec \alpha \), then the area of the triangle formed by the asymptotes of the hyperbola with any of its tangent is:
The equation of the pair of asymptotes of the hyperbola \( 4x^2 - 9y^2 - 24x - 36y - 36 = 0 \) is:
If \( e_1 \) and \( e_2 \) are respectively the eccentricities of the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and its conjugate hyperbola, then the line \( \frac{x}{2e_1} + \frac{y}{2e_2} = 1 \) touches the circle having center at the origin, then its radius is:
The equation of one of the tangents drawn from the point \( (0,1) \) to the hyperbola \( 45x^2 - 4y^2 = 5 \) is:
If \( y = x + \sqrt{2} \) is a tangent to the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \), then equations of its directrices are:
Evaluate \( \cosh (\log 4) \):
If \( \tanh x = \text{sech } y = \frac{3}{5} \) and \( e^{x+y} \) is an integer, then \( e^{x+y} \) is:

The descending order of magnitude of the eccentricities of the following hyperbolas is: 
A. A hyperbola whose distance between foci is three times the distance between its directrices. 
B. Hyperbola in which the transverse axis is twice the conjugate axis. 
C. Hyperbola with asymptotes \( x + y + 1 = 0, x - y + 3 = 0 \).

Let origin be the centre, \((\pm 3,0)\) be the foci and \(\dfrac{3}{2}\) be the eccentricity of a hyperbola. Then the line \(2x-y-1=0\)
The locus of a variable point whose chord of contact with respect to the hyperbola
\[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] subtends a right angle at the origin is