Question

for a circle of radius 4 with center (-4, 3). in general form

Answer 1

Reduced Equation:

$(x-x_o)^2+(y-y_o)=r^2\\ \\ (x+4)^2+(y-3)^2=16\\ \\ x^2+8x+16+y^2-6y+9-16=0\\ \\ \boxed{x^2+y^2+8x-6y+9=0}$

Answer 2

I'm going to assume that you're asking for the equation of that circle.
It's

(x + 4)² + (y - 3)² = 16