# Lesson and Practice: Circle and Coordinate Geometry

- Author:
- Simona Riva

Discover how to write the equation of a circle given its center and radius, and how to find center and radius given the general equation of a circle.
Explore the applet, then answer the questions displayed below.

Select the option "Circle - given center and radius" in the app above, then drag the center C at (0,0).
Use the slider to display different circles with center at (0,0).
What is the equation of a circle with center at (0,0) and radius *r*?

A circle with center *C*=(0,0) passes through *P*=(2,3). What is the equation of the circle?

Given *A*=(-8,-3) and *B*=(2, 5), write the equation of the circle with diameter *AB*.

Select the option "Circle - general equation" in the applet above and use the sliders to explore the equation and the corresponding graph. When ...

When ...

When ...

When ...

Does the equation represent a circle? If so, determine its center and radius. If not, explain why this is not the equation of a circle.