### Unit 10: Introduction to Conic Sections

Conic sections are made by taking particular slices of a cone. The slices we will study include ellipses, hyperbolas, and parabolas. You will have studied parabolas in the context of functions previously in the course, but these parabolas are different because they are not functions. Read on to learn more!

**Completing this unit should take you approximately 2 hours.**

Upon successful completion of this unit, you will be able to:

- write the equation of ellipses, hyperbolas, and parabolas in standard form; and
- graph ellipses, hyperbolas, and parabolas centered on and off the origin.

### 10.1: Ellipses

First, we will focus on ellipses and the components that make up the equation for an ellipse. You will learn how to write the equation of an ellipse given different components of the ellipse.

This section will focus on graphing ellipses given equations that are either centered at the origin or not centered at the origin.

### 10.2: Hyperbolas

Hyperbolas can be constructed by intersecting a right circular cone with a plane at an angle where both cone halves intersect. In this section, you will explore the characteristics of hyperbolas and use them to construct hyperbola equations. We will focus on whether or not the hyperbolas are centered at the origin.

This section will focus on graphing hyperbolas given equations that are centered at the origin and those that are not.

### 10.3: Parabolas

Parabolas can be constructed when a plane cuts through a right circular cone. If the plane is parallel to the edge of the cone, a parabola is formed. In this section, you will explore the characteristics of parabolas and use them to construct equations of parabolas. Note that these are not the parabolas we studied before because they are not functions.

This section will focus on graphing parabolas given equations not centered at the origin.