Graphing Circles on the Coordinate Plane Solutions

• To sketch a circle on a coordinate plane:

  • Graph the    center    of the circle.

  • Use the    radius    to determine the horizontal and vertical points of the circle. 

  • Sketch a    curve    between the points.

Note

A compass could also be used to help graph the circle but is not required.

• The    general form    of the equation of a circle is: $x^2+y^2+Dx+Ey+F=0$
• For this lesson, write all circles in standard form so the values of     h, k, and the radius r    are known.

• Convert the equation of a circle from general to    standard    form by completing the square with    both x and y   .

Note

When the equation of a circle is written in the general form, the coefficient of $x^2$ and$y^2$ must be the same. You will learn why in the lesson on ellipses.

Example 5

Graph and write the equation of a circle with a domain of $\left\{\mathit{x}|\mathit{x}\in ℝ, –3\le \mathit{x}\le 5\right\}$ and a range of $\left\{\mathit{y}|\mathit{y}\in ℝ, –7\le \mathit{y}\le 1\right\}$.

Example 6

Graph: $\mathbf{3}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{3}{\mathit{y}}^{\mathbf{2}}\mathbf{+}\mathbf{9}\mathit{x}\mathbf{–}\mathbf{6}\mathit{y}\mathbf{–}\frac{\mathbf{9}}{\mathbf{4}}\mathbf{=}\mathbf{0}$

Note

It is not required to write down the center and radius because it is part of the equation written in standard form.