16. Parametric Equations & Polar Coordinates

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

Graph the ellipse $\(\frac{\left(x-1\right)^2}{9}\)+\(\frac{\left(y+3\right)^2}{4}\)=1$.

Given the hyperbola $\(\frac{x^2}{25}\)-\(\frac{y^2}{9}\)=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$.

A vertically oriented 3D cone is sliced with a vertical 2D plane. What is the conic section that will form?

Find the standard form of the equation for an ellipse with the following conditions.

Foci = $\(\left\)(-5,0\(\right\)),\(\left\)(5,0\(\right\))$

Vertices = $\(\left\)(-8,0\(\right\)),\(\left\)(8,0\(\right\))$

Determine if the equation $x^3+y^2+4x-8y+4=0$ is a circle, and if it is, find its center and radius.

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

Determine if the equation $x^2+y^2-2x+4y-4=0$ is a circle, and if it is, find its center and radius.

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

Given the equation $\(\frac{x^2}{4}\)+\(\frac{y^2}{9}\)=1$, sketch a graph of the ellipse.

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

Sketch a graph of the circle based on the following equation: $\(\left\)(x-2\(\right\))^2+\(\left\)(y+3\(\right\))^2=1$