The standard equation of a circle is given by: [math]\left(x-h\right)^2+\left(y-k\right)^2=r^2[/math] [br]This should remind you of the pythagorean theorem: [math]a^2+b^2=c^2[/math]

Note that when a circle equation contains a negative, h and k are actually positive values. [br][br]for the circle [math]\left(x-5\right)^2+\left(y+2\right)^2=16[/math], the center of the circle would be (h,k)=(5,-2), with a radius of 4, since[math]4^2=16[/math][br][br]Now use the geogebra applet to see how manipulating the center and radius of a circle changes the equation of a circle in real time.