"find the equation of the sphere passing through (1,2,3),(-1,3,5),(2,-3,5),(2,1,0)"?

Answer 1

The basic idea is this.

You're looking for a equation of the form (x-a)^2 + (y-b)^2 + (z-c) ^2 = r^2.

Each known point gives you a quadratic equation in a, b, c, and r. Four points gives you four simultaneous equations.

Take one equation, and subtract it in turn from each of the other three. What will be left over will be three simultaneous LINEAR equations in a, b, and c. Solve them. Substitute back in and get d. Check your work. And you'll be done!

Answer 2

Please specify the fourth point. It is not fully printed.