19. Conic Sections

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

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

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

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

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\(\right\))$.

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

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