How Do You Graph a Circle?

How Do You Graph a Circle?

The equation to graph a circle is written in the standard form (x - h)^2 + (y-k)^2 = r^2, where the ordered pair (h, k) is the center of the circle and r is the radius. To get the equation to this form, you may need to complete the square.

  1. Convert the equation to standard form

    For example, assume you have the equation x^2 + y^2 - 12x - 4y + 36 = 0. To complete the square, group like terms together in their own parenthesis, halve the coefficents, and square them to yield the final terms of the squares. In the example, this is (x^2 - 12x + 36) + (y^2 - 4y + 4) = -36. Add both the terms you just found to the right side of the equation, giving you 4. Converted to standard form, the equation is (x - 6)^2 + (y - 2)^2 = 4.

  2. Place the center of the circle at the point provided, and find the radius

    In the equation, (h, k) is (6, 2). Place a point at this location on the graph. Take the square root of the radius, which in this case is 2.

  3. Plot the four points of the circle

    Place two points to the right and left and two above and below the center at the appropriate radius. Draw a circle that passes through all four of these points, or use a compass if you need to be precise.