If each point of the circle \(x^2 + y^2 = 25\) is reflected in the point (4,1) the set of image points satisfies the equation \(x^2 + ay^2 + bx + cy + d = 0\). Compute the ordered quadruple \((a,b,c,d)\) of real numbers.
The quadruple (a,b,c,d) is (-8,1,3,5).