Question 11418
You use the standard form for the equation of a circle with center at (h, k) and radius of r.

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

You know where the center is: (-3, 4) so that h = -3 and k = 4 Plug these into the formula:

{{{(x-(-3))^2 + (y-4)^2 = r^2}}}
{{{(x+3)^2 + (y-4)^2 = r^2}}} Now you need to find the radius r.

The radius is just the distance form the circle center to a point on the circumference.  You have the location of the center (-3, 4) and the location of a point on the circumference (4, 6).

You can use the distance formula to find the length of the radius using these two points:

{{{d = sqrt((x2-x1)^2 + (y2-y1)^2)}}}
{{{d = sqrt((4-(-3))^2 + (6-4))^2)}}}
{{{d = sqrt(7^2 + 2^2)}}}
{{{d = sqrt(49 + 4)}}}
{{{d = sqrt(53)}}} This is the length of the radius r, but you really want r^2, so you will square both sides of this.

{{{d^2 = 53}}}

The equation for your circle is:

{{{(x+3)^2 + (y-4)^2 = 53}}}