How to Put Circle Equation Into Graphing Calculator

Standard Form of a Circle

The standard form of a circle equation is:

Where:

• (h, k) is the center of the circle
• r is the radius of the circle

This form is essential because it clearly identifies the circle's center and radius, which are critical for graphing.

Steps to Graph a Circle

1. Identify the Center and Radius

   From the equation (x - h)² + (y - k)² = r², identify the values of h, k, and r.

2. Plot the Center

   Locate the center point (h, k) on the coordinate plane.

3. Draw the Radius

   Use the radius r to draw a circle centered at (h, k).

4. Verify the Graph

   Check that the graph passes through the points (h + r, k), (h - r, k), (h, k + r), and (h, k - r).

Worked Example

Let's graph the circle (x - 2)² + (y + 3)² = 25.

1. Identify h = 2, k = -3, and r = 5.
2. Plot the center at (2, -3).
3. Draw a circle with radius 5 centered at (2, -3).
4. Verify by checking points (7, -3), (-3, -3), (2, 2), and (2, -8).

Common Errors

• Forgetting to square the radius when converting from general form
• Misidentifying the center coordinates
• Incorrectly plotting the radius on the graph
• Assuming the circle is always centered at the origin