A series of free, online video lessons with examples and solutions to help Algebra students learn about circle conic sections.

**Related Pages**

Conic Sections: Circles 2

Conic Sections: Ellipses

Conic Sections: Parabolas

Conic Sections: Hyperbolas

The following diagram shows how to derive the equation of circle (x - h)^{2} + (y - k)^{2} = r^{2} using Pythagorean Theorem and distance formula. Scroll down the page for examples and solutions.

When working with circle conic sections, we can derive the equation of a circle by using coordinates and the distance formula.

The equation of a circle is (x - h)^{2} + (y - k)^{2} = r^{2} where r is equal to the radius, and the coordinates (x,y) are equal to the circle center.

The variables h and k represent horizontal or vertical shifts in the circle graph.

Examples:

1. Find the center and the radius

a) x^{2} + (y + 2)^{2} = 121

b) (x + 5)^{2} + (y - 10)^{2} = 9

2. Find the equation the circle with

a) center(-11, -8) and radius 4

b) center (2, -5) and point on circle(-7, -1)

Identify the equation of a circle.

Write the standard form of a circle from general form.

Graph a circle.

A circle is the set of points (x,y) which are a fixed distance r, the radius, away from a fixed point (h,k), the center.

(x - h)^{2} + (y - k)^{2} = r^{2}

Examples:

1. Graph the circle

a) (x - 3)^{2} + (y + 2)^{2} = 16

b) x^{2} + (y - 1)^{2} = 4

2. Write in standard form and then graph

2x^{2} + 2y^{2} - 12x + 8y - 24 = 0

Introduction to Circles

Understand the equation of a circle

Example:

Graph the equation

(x - 1)^{2} + (y + 2)^{2} = 9

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