Question 261409
<pre><font size = 4 color = "indigo"><b>
To get the equation of a circle we need the center (h,k)
and the radius r, and the standard equation for a circle

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


We have the center point, so all we need is the radius.

Let's plot the center (-4,-7) and draw the line {{{x=2}}} which is
a vertical line through 2 on the x-axis, shown in green below:

{{{drawing(400,400,-12,4,-13,3, graph(400,400,-12,4,-13,3),locate(-4,-7,"(-4,-7)"),
line(-4+.1,-7,-4-.1,-7), line(-4,-7+.1,-4,-7-.1), line(-4+.1,-7+.1,-4-.1,-7-.1), line(-4+.1,-7-.1,-4-.1,-7+.1), green(line(2,-15,2,4))   )}}} 

We draw a horizontal line from the center over to where the
circle is to be tangent to the green line, for that will be a
radius for the circle, which we can also draw in::

{{{drawing(400,400,-12,4,-13,3, graph(400,400,-12,4,-13,3),locate(-4,-7,"(-4,-7)"), red(line(-4,-7,2,-7)), circle(-4,-7,6),
line(-4+.1,-7,-4-.1,-7), line(-4,-7+.1,-4,-7-.1), line(-4+.1,-7+.1,-4-.1,-7-.1), line(-4+.1,-7-.1,-4-.1,-7+.1), green(line(2,-15,2,4))   )}}}

Using the x-axis as a measuring stick, we can see that that radius
is 6 units long, 4 units over to the y-axis and 2 units more on the
right side of the y-axis, which makes the radius 6 units long.  So
all that's left to do is substitute (h,k)= (-4,-7), and r=6 into the 
standard equation for a circle:

{{{(x-(-4))^2+(y-(-7))^2=(6)^2}}}
{{{(x+4)^2+(y+7)^2=36}}}

That's it.

Edwin</pre>