Thread: distance between a pt. to sphere

1. distance between a pt. to sphere

how will i calculate the smallest and largest distances between the point(1,1,1) and the sphere
$x^2+y^2+z^2-2y+6z-6=0$ ?

2. Originally Posted by ramiee2010
how will i calculate the smallest and largest distances between the point P(1,1,1) and the sphere
$x^2+y^2+z^2-2y+6z-6=0$ ?
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 $d = |\overline{CP}|$

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.