Videos and lessons with examples and solutions to help High School students derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Related Topics:Common Core Geometry

Common Core Mathematics

Common Core: HSG-GPE.A.1

The following figure shows how to derive the equation of a circle. Scroll down the page for more examples and solutions.This lesson shows two examples regarding how to find the equation of a circle centered at the origin.

Examples:

1. Determine an equation for a circle with radius 3 units and centered at the origin.

2. Determine an equation for the circle through the point (-3,4) with center at the origin.

3. Check to see if each of the following points is on, inside or outside the circle for example 2.

a) (2, -3)

b) (1, 5)

c) (-4, -3)

Example:

Graph the circle x

Example:

The equation of a circle C is (x + 3)

What is its center (h, k) and its radius r?

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