Acircle is centered at the point (5, -4) and passes through the point (-3, 2).
the equation of this circle is (x + blank )2 + (y + blank)2 = blank.
fill out the blanks.

Equation of circle : (x-h)² + (y-k)² = R², where h and k are the coordinates of the circle and R, THE RADIUS

Center coordinates (5,-4), hence

(x-5)² + (y+4)² =R²

Now let's calculate R.  Just replace x and y by the coordinates (-3,2)

(-3-5)² + (2+4)² = 10², so the Radius is equal to 10 and the final shape:

(x-5)² + (y+4)² = 100