1. Conic Sections
Anyway you slice it

2. Properties of Cone generate cone
A cone is created by rotating a line called the generator around an axis.
The greater the slope of the line the skinnier the cone
generate cone

3. Definition:
A conic section is the intersection of a plane and a Double Cone.
By changing the angle and location of intersection, we can produce
1. circle,
2. ellipse,
3. parabola
4. hyperbola;

4. How to get Shapes
1. plane perpendicular to axis of cone – circle (horizontal plane)
2. not perpindicular only intersect one nappe –
A. ellipse
B. Parabola – parallel to generating line
3. plane intersecting both nappes – hyperbola
Slice cone

5. Equations of Conic Sections
General Equation of all conic sections
We will examine different forms of this quadratic relation

6. Equation in Vertex Form
Circle
Ellipse
Parabola
Hyperbola

7. Translations (h, k) Center (vertex)
Circle
Ellipse
Parabola
Hyperbola

8. Parabola – only 1 variable squared
Hyperbola – both variables squared, different coefficients (divided by different numbers) and subtracted
Circle – both variables squared, addition – coeffecients same
Ellipse – both variables squared, addition, coefficients different (divided by different numbers)

9. Conics in Real Life
Ellipse
Hyperbola
Parabola
Circle

10. Degenerate Conic Sections
Point – horizontal plane cuts cone at vertex
Line – plane cuts the cone exactly on the generator
Intersecting Lines – plane cuts the cone exactly on the vertical axis