I have to calculate themaximumdistance from the point $\displaystyle T(1, -1, 3)$ to the sphere $\displaystyle x^2+y^2+z^2-6x+4y-10z-62=0$.

Here's what I did.

The equation for the sphere is $\displaystyle (x-3)^2+(y+2)^2+(z-5)^2=100$.

That means the center of the sphere is $\displaystyle C(3, -2, 5)$, and the radius is $\displaystyle r=10$.

I think the maximum distance $\displaystyle d_m$ is the distance from the point $\displaystyle T$ to the center of the sphere plus the radius:

$\displaystyle d_m=d(T, C)+r$.

Is this okay?

Please advise.

Thank you!