Equations of Circles

What is the formula for an equation of a circle?

Let (x, y) represent a point on a circle centered at the origin.

Determine the equation of the circle and justify your reasoning.

• The equation of the circle is (x + y)² = r² because the curvature of the circle is formed by a quadratic relationship.

• The equation of the circle is x² + y² = r² because the Pythagorean Theorem can be used to describe all points equidistant from the origin with a radius of r.

• The equation of the circle is x + y = r because the radius of the circle is always equal to the sum of the x and y coordinates.

• The equation of the circle is x² + y² = r because the distance formula can be used to determine all points equidistant from the origin with a radius of r.

Point B is located on circle A, as shown below.

Determine the equation of circle A.

Determine the equation for the graphed circle.

Determine the equation of the given circle.

Determine the equation of the circle.

When graphed, circle C has a diameter with endpoints on the circle at points A and B .

Which is the correct equation for circle C ?

What is the equation of the circle with a radius of 5 and center at (2, 3)?

Given a circle with the equation

(x−2)²+(y+6)²=36 ,

which of the following represents the center and radius of the circle?

• center (−2, 6); radius = 6

• center (2, -6); radius = 6

• center (−2, 6); radius = 36

• center (2, -6); radius = 36

A circle is represented by the equation 

(x−1)²+(y+5)²=6 . Which of the following shows the location of the center of the circle and its radius?