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-Khan Academy