16. Parametric Equations & Polar Coordinates

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

Graph the parabola $-4\(\left\)(y+1\(\right\))=\(\left\)(x+1\(\right\))^2$, and find the focus point and directrix line.

If a parabola has the focus at $\(\left\)(0,-1\(\right\))$ and a directrix line $y=1$, find the standard equation for the parabola.

Graph the parabola $8\(\left\)(x+1\(\right\))=\(\left\)(y-2\(\right\))^2$ , and find the focus point and directrix line.

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.