# Distinguishing Conic Sections From Graphing Format

Let's review the patterns for each conic section:

Circle: (x-h)

Parabola:

^{2}+(y-k)^{2}=r^{2}Parabola:

Let's note a few key differences:

To complete the square for ellipses and hyperbolas:

- Parabolas only have one squared variable. (For all the others, both the x and y are squared.)
- Circles do not have fractions/denominators. Also, they may or may not equal 1.
- Ellipses have different denominators and equal 1. There is a plus sign in between the fractions.
- Hyperbolas also have different denominators and equal 1, but there is a negative sign in between the fractions.

Let's identify a few conic sections:

This is an ellipse because both variables are squared, it contains fractions, it equals 1, and there is a plus sign in between the fractions.

This is a circle. You can tell because both variables are squared but there are not fractions.

This is a hyperbola because both variables are squared, it contains fractions, it equals 1, and there is a negative sign in between the fractions.

We know this is a parabola because only the y is squared.

Identify each equation as a parabola, circle, ellipse, or hyperbola.**Answers:**1) parabola 2) hyperbola 3) ellipse 4) circle 5) hyperbola

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