# 7.1: Introduction to Conics

- Page ID
- 4017

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

In this chapter, we study the **Conic Sections** - literally `sections of a cone'. Imagine a double-napped cone as seen below being `sliced' by a plane.

If we slice the cone with a horizontal plane the resulting curve is a **circle**.

Tilting the plane ever so slightly produces an **ellipse**.

If the plane cuts parallel to the cone, we get a **parabola**.

If we slice the cone with a vertical plane, we get a **hyperbola**.

If the slicing plane contains the vertex of the cone, we get the so-called `degenerate' conics: a point, a line, or two intersecting lines.

We will focus the discussion on the non-degenerate cases: circles, parabolas, ellipses, and hyperbolas, in that order. To determine equations which describe these curves, we will make use of their definitions in terms of distances.

### Contributors

- Carl Stitz, Ph.D. (Lakeland Community College) and Jeff Zeager, Ph.D. (Lorain County Community College)