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

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

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

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

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

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

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

Find the equation for the following circle:

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