First use the coordinate of the center to start building your equation. The equation of a circle recall is
[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
With the center point being (h,k).
Once you put in the centers coordinates, your equation should be,
[tex] {(x + 3)}^{2} + {(y - 4)}^{2} = {r}^{2} [/tex]
However we still need to find the radius. We can do this using the second point given, by putting it into the equation and solving for the radius.
[tex] {( 4 + 3)}^{2} + {( - 2 - 4)}^{2} = {r}^{2} [/tex]
Solving this gives us the final part of the equation.
[tex]85 = {r}^{2} [/tex]
And we can finally put our full equation together,
[tex] {(x + 3)}^{2} + {(y - 4)}^{2} = 85[/tex]
