Graphing a Circle

Graph the equation \(( x+3) ^{2}+( y-2) ^{2}=16\).

Solution  This is the standard form of an equation of a circle. To graph the circle, we first identify the center and the radius of the circle. \begin{eqnarray*} ( x+3) ^{2}+( y-2) ^{2}&=&16\\[0pt] ( x-( \underset{\underset{\color{#0066A7}{h}}{\color{#0066A7}{\uparrow}}}{-3}))^{2} +( y-\underset{\underset{\color{#0066A7}{k}}{\color{#0066A7}{\uparrow}}}{2})^{2}&=&\underset{\underset{\color{#0066A7}{r^2}}{\color{#0066A7}{\uparrow}}}{4^{2}}\\[0pt] \end{eqnarray*}

The circle has its center at the point\( ( -3, 2) ;\) its radius is \(4\) units. To graph the circle, we plot the center \(( -3, 2) .\) Then we locate the four points on the circle that are \(4\) units to the left, to the right, above, and below the center. These four points are used as guides to obtain the graph. See Figure 35.