Hyperbola · Mathematics · COMEDK

The foci of a hyperbola are the same as those of the ellipse with equation $9 x^2+16 y^2=144$.

If the length of the transverse axis of this hyperbola is $2 \cos \alpha$, then its equation is:

The difference between the distance of any point on the hyperbola from the two foci is $\mathbf{1 6}$ and the eccentricity is $\mathbf{2}$. Then the equation of the hyperbola is

If the distance between the foci and the distance between the two directrixes are in the ratio $$3: 2$$ for a hyperbola $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$, then a : b is

The distance between the foci of a hyperbola is 16 and its eccentricity is $$\sqrt{2}$$. Then its equation is

If $${{{x^2}} \over {36}} - {{{y^2}} \over {{k^2}}} = 1$$ is a hyperbola, then which of the following statements can be true?