1. Notes 8.1 Conics Sections – The Parabola

2. I. Introduction
A.) A conic section is the intersection of a plane and a cone.
B.) By changing the angle and the location of intersection, a parabola, ellipse, hyperbola, circle, point, line, or a pair of intersecting lines is produced.

3. C.) Standard Conics:
1.) Parabola
2.) Ellipse
3.) Hyperbola

4. D.) Degenerate Conics 2.) Point 3.) Line 4.) Intersecting Lines
1.) Circle
2.) Point
3.) Line
4.) Intersecting Lines

5. E.) Forming a Parabola –
When a plane intersects a double-napped cone and is parallel to the side of the cone, a parabola is formed.

6. F.) General Form Equation for All Conics
If both B and C = 0, or A and B = 0, the conic is a parabola

7. II. The Parabola
A.) In general - A parabola is the graph of a quadratic equation, or any equation in the form of

8. B.) Def. - A 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.

9. Axis of Symmetry
Focus
Focal Width
Vertex
Focal Length
Directrix

10. C.) Parabolas (Vertex = (0,0))
Standard Form
Focus
Directrix
Axis of Symmetry
Focal Length
Focal Width

11. D.) Ex. 1- Find the focus, directrix, and focal width of the parabola y = 2x2.

12. E.) Ex. 2- Do the same for the parabola
Focus =
Directrix =
Focal Width =

13. F.) Ex. 3- Find the equation of a parabola with a directrix of x = -3 and a focus of (3, 0).

14. G.) Parabolas (Vertex = (h, k))
St. Fm.
Focus
Directrix
Ax. of Sym.
Fo. Lgth.
Fo. Wth.

15. H.) Ex. 4- Find the standard form equation for the parabola with a vertex of (4, 7) and a focus of (4, 3).

16. I.) Ex. 5- Find the vertex, focus, and directrix of the parabola 0 = x2 – 2x – 3y – 5.

17. III. Paraboloids of Revolution
A.) A PARABOLOID is a 3-dimensional solids created by revolving a parabola about an axis.
Examples of these include headlights, flashlights, microphones, and satellites.

18. B.) Ex. 6– A searchlight is in the shape of a paraboloid of revolution. If the light is 2 feet across and 1 ½ feet deep, where should the bulb be placed to maximize the amount of light emitted?

19. The bulb should be placed 2” from the vertex of the paraboloid