8. Conic Sections

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?

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

Identify each equation without completing the square.

$y^2-4x-4y=0$

Identify each equation without completing the square.

$9x^2+25y^2-54x-200y+256=0$

Identify each equation without completing the square.

$9x^2+4y^2-36x+8y+31=0$

Identify each equation without completing the square.

$y^2+8x+6y+25=0$

Without actually graphing, identify the type of graph that each equation has.

$\frac{x^2}{4}-\frac{y^2}{16}=1$