Find an equation for the circle that has center (−3, 4) and passes through the point (4, −2).

First use the coordinate of the center to start building your equation. The equation of a circle recall is

With the center point being (h,k).

Once you put in the centers coordinates, your equation should be,

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.

Solving this gives us the final part of the equation.

And we can finally put our full equation together,