Show that the equation to a sphere passing through three points (2,0,0),(0,2,0) and (0,0,2) and having its centre on the plane $2x+3y+4z=27$ is $x^2+y^2+z^2-6x-6y-6z+8=0.$

Question

This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com