Chapter 8.1

Conic Sections and Parabolas Learning Target: I can find the equation, focus, and directrix of a parabola.

Definition • Conic Section – a cross section of a cone (the intersection of a plane with a right circular cone) • The three basic conic section are parabola, ellipse, and hyperbola.

Parabola

Ellipse

Hyberbola

Point

Line

Intersecting Line

Can you think of any shape we are missing?

• Circle • The reason we do not see a circle is because it is a special kind of ellipse.

Parabola • Is the set of all points in a plane equidistant from a particular line (the directrix) and a particular point (the focus) in the plane.

Algebraically • Conic sections can be defined algebraically as the graphs of second degree (quadratic) equations in two variable in the form: • Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 • where A, B, and C are not all zero.

Homework None