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?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.