Find the expanded form of the circle equation with center at point \((h, k) = (-3, 4)\) and radius \(r = 5\)

Step 1 ：We know that the standard equation of a circle is \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius of the circle.

Step 2 ：Substitute \(h=-3\), \(k=4\), and \(r=5\) into the equation to get \((x-(-3))^2 + (y-4)^2 = 5^2\) or \((x+3)^2 + (y-4)^2 = 25\).

Step 3 ：Expand the equation to get \(x^2 + 6x + 9 + y^2 - 8y + 16 = 25\).

Step 4 ：Simplify the equation to get \(x^2 + y^2 + 6x - 8y = 0\).