If $(4, 0)$ and $(-4, 0)$ are the vertices and $(6, 0)$ and $(-6, 0)$ are the foci of a hyperbola,then its eccentricity is

The line $3x - 4y = 5$ is a tangent to the hyperbola $x^2 - 4y^2 = 5$. The point of contact is

Let $P, Q, R, S$ be the points of intersection of the circle $x^2+y^2=4$ and the hyperbola $xy=\sqrt{3}$. If $P=(\alpha, \beta)$ and $\alpha>\beta>0$,then the equation of the tangent drawn at $P$ to the hyperbola is

Let $x^2+y^2=16$ be the equation of the auxiliary circle of a hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and let $(4 \sqrt{2}, 3)$ be a point on the hyperbola. Then,the eccentricity of the hyperbola is

The eccentricity of the hyperbola $-\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is:

The circle $x^2 + y^2 - 8x = 0$ and the hyperbola $\frac{x^2}{9} - \frac{y^2}{4} = 1$ intersect at points $A$ and $B$. The line $2x + y = 1$ is a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If this line passes through the point of intersection of the nearest directrix and the $x$-axis,find the eccentricity of the hyperbola.