how will i calculate the smallest and largest distances between the point(1,1,1) and the sphere
$\displaystyle x^2+y^2+z^2-2y+6z-6=0$ ?
1. Determine the coordinates of the center C of the sphere and the length of the radius r by completing the squares.
2. Determine the distance $\displaystyle d = |\overline{CP}|$
3. Then the shortest distance of P to the sphere is d - r
and the longest distance of P to the sphere is d + r.