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