16. Parametric Equations & Polar Coordinates

If a parabola has the focus at $\left(2,4\right)$ and a directrix line $x=-4$ , find the standard equation for the parabola.

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 $\frac{y^2}{16}-\frac{x^2}{9}=1$.

Describe the hyperbola $\frac{\left(x+2\right)^2}{9}-\frac{\left(y-4\right)^2}{16}=1$.

Describe the hyperbola $y^2-\frac{\left(x-1\right)^2}{4}=1$.

31–38. Equations of parabolas Find an equation of the following parabolas. Unless otherwise specified, assume the vertex is at the origin.

31–38. Equations of parabolas Find an equation of the following parabolas. Unless otherwise specified, assume the vertex is at the origin.

31–38. Equations of parabolas Find an equation of the following parabolas. Unless otherwise specified, assume the vertex is at the origin.

A parabola that opens to the right with directrix x = -4

31–38. Equations of parabolas Find an equation of the following parabolas. Unless otherwise specified, assume the vertex is at the origin.

A parabola with focus at (3, 0)

31–38. Equations of parabolas Find an equation of the following parabolas. Unless otherwise specified, assume the vertex is at the origin.

A parabola symmetric about the y-axis that passes through the point (2, -6)