Question 134822
If you know the coordinates of the center of the circle and the radius of the circle, you can write the equation of the circle from that information.  Just looking at the graph will give you that information presuming the center point coordinates and the radius are nice neat integers, or the coordinates and radius are labeled.


If the center is at (h,k) and the radius is r, then the equation of the circle is {{{(x-h)^2+(y-k)^2=r^2}}}


Example:

{{{drawing(600,600,-6,6,-6,6,
grid(1),
green(circle(-1,2,3)),
circle(-1,2,.05),
locate(-1.3,1.7,C(-1,2)),
red(line(-1,2,-4,2),
line(-4,2,-3.8,2.2),
line(-4,2,-3.8,1.8),
line(-1,2,-1.2,2.2),
line(-1,2,-1.2,1.8)),
locate(-2.75,2.4,r=3)
)}}}


Here we have a circle with center at (-1,2) and a radius of 3, so using the general form of the equation and making the appropriate substitutions:


{{{(x-h)^2+(y-k)^2=r^2}}}


{{{(x-(-1))^2+(y-2)^2=3^2}}}


{{{(x+1)^2+(y-2)^2=9}}}


By the way, notice that your unit circle, {{{x^2+y^2=1}}} follows the same pattern.  It is a circle with center at (0,0) and radius 1, so:


{{{(x-0)^2+(y-0)^2=1^2}}}


{{{x^2+y^2=1}}}


Not sure I answered your question.  Write back with an example problem if you need more help.

John