Definition and Terms Involving Hyperbola

Find the equation of the directrix of the hyperbola $\frac{x^2}{25}-\frac{y^2}{16}=1$

Find the equation of the directrix of the hyperbola $\frac{x^2}{25}-\frac{y^2}{9}=1$

Find the equation of the directrix of the hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$

The hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ passes through the point of intersection of the lines $7x+13y-87=0 \mathrm{and} 5x-8y+7=0$ and its latus rectum is of length $\frac{32\sqrt{2}}{5}$. Eccentricity is $\frac{\sqrt{m}}{5}$. Find $m$.

Sum of the lengths of transverse axis and conjugate axis of the following hyperbola $y^2-16x^2=16$ is

Find the sum of the lengths of transverse axis and conjugate axis of the hyperbola $y^2-36x^2=36$.

Find the sum of the lengths of transverse axis, conjugate axis, and the latus-rectum of the hyperbola $16y^2-4x^2=1$.

Find the sum of the lengths of transverse axis, conjugate axis, and the latus-rectum of the hyperbola $16x^2-9y^2=576$.

If the coordinates of foci of the hyperbola $49y^2-16x^2=784$ are of the form $\left(0,\pm \sqrt{k}\right)$ then find the value of $k$.

If the coordinates of foci of the hyperbola $\frac{y^2}{9}-\frac{x^2}{27}=1$ are of the form $\left(0,\pm k\right)$ then find the value of $k$.

If the eccentricity of the hyperbola $y^2-x^2=1$ is $\sqrt{k}$ then find the value of $k$.

Find the sum of the lengths of transverse axis and conjugate axis of the hyperbola $y^2-16x^2=16$.

Find the eccentricity of the hyperbola $9x^2-16y^2=144$.

If the coordinates of the foci of the hyperbola $16x^2-9y^2=144$ are of the form $\left(\pm k,0\right)$ then find the value of $k$.

If the coordinates of the foci of the hyperbola $\frac{y^2}{9}-\frac{x^2}{27}=1$ are of the form $\left(0,\pm k\right)$ then find the value of $k$.

Find the length of the latus-rectum of the hyperbola $16x^2-9y^2=576$.

Find the sum of the lengths of transverse axis and conjugate axis of the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=1$.

Find foci, eccentricity, equations of directrix and length of latus rectum of the hyperbla $x^2-4y^2=4$

For next two question please follow the same

 Let $\mathrm{P}\left(\mathrm{x}, \mathrm{y}\right)$ is a variable point such that $\left|\sqrt{{\left(\text{x}-1\right)}^2+{\left(\text{y}-2\right)}^2}-\sqrt{{\left(\text{x}-5\right)}^2+{\left(\text{y}-5\right)}^2}\right|=3$  which represents hyperbola.

The eccentricity $\mathrm{e}\text{'}$ of the corresponding conjugate hyperbola is

Let $e_1$ and $e_2$ are the eccentricities of the ellipse $\frac{x^2}{18}+\frac{y^2}{4}=1$ and the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ respectively. If $\left(e_1,e_2\right)$ is a point on the ellipse $15x^2+3y^2=k$ , then the value of $k$ is equal to