Write the equation of a circle with center (-2,3) and a radius of 4. Show all work to receive credit.

The equation of the circle is given by:

(x-a) ^2 + (y-b) ^2=r^2

where:

(a, b) is the center of the circle

given that the center of our circle is (-2,3) with the radius of 4, the equation will be:

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

expanding the above we get:

x^2+4x+4+y^2-6y+9=16

this can be simplified to be:

x^2+4x+y^2-6y=16-13

x^2+y^2+4x-6y=3