The equation $\frac{1}{r} = \frac{1}{8} + \frac{3}{8} \cos \theta$ represents:

If $ax^{2}+2hxy+by^{2}+2gx+2fy+c=0$ represents a joint equation of the directrices of the hyperbola $16x^{2}-9y^{2}=144$,then $g+f-c=$

The line $2x + y = 1$ is a tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ $(a > b)$. If this line passes through the point of intersection of a directrix and the positive $X$-axis,then the eccentricity of that hyperbola is

Find the equation of the hyperbola satisfying the given conditions: Vertices $(\pm 2, 0)$,foci $(\pm 3, 0)$.

The locus of a point of intersection of two lines $x \sqrt{3}-y=k \sqrt{3}$ and $\sqrt{3} k x+k y=\sqrt{3}$,where $k \in R$,describes:

The eccentricity of the hyperbola $4x^2 - 9y^2 = 36$ is