16. Parametric Equations & Polar Coordinates

Sketch a graph of the circle based on the following equation: $x^2+\(\left\)(y-1\(\right\))^2=9$

How can you slice a vertically oriented 3D cone with a 2D plane to get a circle?

Determine the vertices and foci of the following ellipse: $\(\frac{x^2}{9}\)+\(\frac{y^2}{16}\)=1$.

Given the ellipse equation $\(\frac{x^2}{16}\)+\(\frac{y^2}{4}\)=1$, determine the magnitude of the semi-major axis (a) and the semi-minor axis (b).

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

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

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

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

How can you slice a vertically oriented 3D cone to get a 2D parabola?

Determine the vertices and foci of the following ellipse: $\(\frac{x^2}{49}\)+\(\frac{y^2}{36}\)=1$.

Find the equation for the following circle:

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

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

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