Acircle is centered at the point (5 -4) and passes through the point (-3,2) the equation of this circle is (x+_)^2+(y+_)^2=_

A circle centered at (h, k) with radius r will have equation ...

... (x -h)² + (y-k)² = r²

The point satisfies the equation for the circle. Filling in the given numbers, we have ...

... (x -5)² + (y+4)² = (-3-5)² + (2+4)² . . . . . . (h, k) = (5, -4), (x, y) = (-3, 2)

... (x -5)² + (y +4)² = 64 +36

The equation of the circle is ...

... (x -5)² + (y +4)² = 100