Equation of the sphere that passes through 4 points Write he equation of the sphere that passes through points
$$a(-5,4,1),b(3,4,-5),c(0,0,4),d(0,0,0)$$
I tried to use four points to draw a geometric shape and then calculate the center of this shape on the basis of the circle that passing  on four points. But I did not succeed

Here is the book answer
  $$x^2+y^2+z^2+54x−58y+4z=0$$


$$\left | \begin{matrix} x^2 + y^2 + z^2 & x & y & z & 1 \\
                         x_1^2 + y_1^2 + z_1^2 & x_1 & y_1 & z_1 & 1 \\
                         x^2_2 + y_2^2 + z_2^2 & x_2 & y_2 & z_2 & 1 \\
                         x_3^2 + y_3^2 + z_3^2 & x_3 & y_3 & z_3 & 1 \\
                         x_4^2 + y_4^2 + z_4^2 & x_4 & y_4 & z_4 & 1                          \end{matrix} \right |  = 0 $$
i.e. $-128(x^2+y^2+z^2-4x-\frac{29}{2}y-4z)=0$
