19. Conic Sections

Given the hyperbola $\frac{x^2}{25}-\frac{y^2}{9}=1$, find the length of the $a$-axis and the $b$ -axis.

Given the hyperbola $x^2-\frac{y^2}{4}=1$, find the length of the $a$ -axis and $b$ -axis.

Given the hyperbola $\frac{y^2}{100}-\frac{x^2}{139}=1$, find the length of the $a$ -axis and the $b$ -axis.

Determine the vertices and foci of the hyperbola $\frac{y^2}{4}-x^2=1$.

Find the equation for a hyperbola with a center at $\left(0,0\right)$, focus at $\left(0,-6\right)$ and vertex at $\left(0,4\right)$.

Find the equations for the asymptotes of the hyperbola $\frac{x^2}{64}-\frac{y^2}{100}=1$.

Find the equations for the asymptotes of the hyperbola $\frac{y^2}{16}-\frac{x^2}{9}=1$.