- Graph circles in standard form
circles
A circle with center [latex](h,k)[/latex] and radius [latex]r>0[/latex] has equation [latex](x-h)^{2}+(y-k)^{2}=r^{2}[/latex].
To graph, plot the center, mark points [latex]r[/latex] units away in the four cardinal directions, and sketch the circle.
Graph [latex]x^{2}+(y+2)^{2}=25[/latex].
Identify center and radius:
[latex]\begin{align} h&=0 \\ k&=-2\\ r^{2}&=25\Rightarrow r=5. \end{align}[/latex]
Plot center [latex](0,-2)[/latex]. Use the center to mark points on the edge of the circle at [latex](0,3), (5,-2), (0,-7), \text{ and } (-5,-2)[/latex].
