Equations of Circles
You can derive the equation of a circle with the help of the Pythagorean Theorem.
Deriving the Equation of a Circle
Pick a point on the circle and draw a right triangle connecting that point with the center of the circle.
The relationship between the sides of the triangle is shown with the Pythagorean Theorem:
Points on the other side of the circle produce triangles with slightly different side lengths:
However, the relationship between the three sides of this triangle is the same, as shown below:
What are the center and radius of the circle described by the equation:
Complete the square to rewrite the equation in graphing form:
Graph the circle from #3.
Graph the following circles:
Find the center and radius of the circle described by each equation.
14. Write the equation of the following circle:
15. Write the equation of the following circle:
To see the Review answers, open this PDF file and look for section 10.2.