Write the equation of the circle that has the center (-3,4) and radius 11.

First we will write the standard for for the circle
equation.

==> (x-a)^2 + (y-b)^2 = r^2 such that
(a,b) is the center and r is the radius.

Given that (-3,4)
is the center and 11 is the radius.

==> (x +3)^2 +
(y-4)^2 = 11^2

Now we will open
brackets.

==> x^2 +6x + 9 + y^2 - 8y + 16 =
121

===> x^2 + y^2 + 6x -8y = 121 -16
-9

==> x^2 + y^2 + 6x -8y =
96

Then the equation of the circle is
:

x^2 + y^2 + 6x - 8y =
96