**A conic section is the intersection of a plane and a cone.**

By changing the angle of the slice you can create a circle, an ellipse, a parabola or a hyperbola

All conic sections have equations of the form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.

Parabola equation: Ax2 + Dx + Ey = 0

Circle equation: x2 + y2 + Dx + Ey + F = 0

Ellipse equation: Ax2 + Cy2 + Dx + Ey + F = 0

Hyperbola equation: Ax2 – Cy2 + Dx + Ey + F = 0

For more on Parabolas see

Conic Sections

Conic Sections-Khan Academy