S6.12.13 Find an equation of the sphere

[karush]

$\tiny{s6.12.13}$$\textsf{Find an equation of the sphere}\\$ $\textsf{that passes through the point (4,3,-1) and has center (3,8,1)} $ \begin{align}\displaystyle(x-3)^2+(y-8)^2+(z-1)^2&= r^2\\\sqrt{(3-4)^2+(8-3)^2+(1+1)^2}&=r^2\\\sqrt{1+25+4}&=\sqrt{30}^2=30 =r\end{align}$\textit{so far ??}$

 

[MarkFL]

What you have is:

\(\displaystyle r=\sqrt{30}\implies r^2=30\)

I would simply write:

\(\displaystyle r^2=(3-4)^2+(8-3)^2+(1+1)^2=30\)

 

[karush]

$\tiny{s6.12.13}$
$\textsf{Find an equation of the sphere}\\$
$\textsf{that passes through the point (4,3,-1) and has center (3,8,1)}$
\begin{align}
\displaystyle
(x-3)^2+(y-8)^2+(z-1)^2&= r^2\\
r^2=(3-4)^2+(8-3)^2+(1+1)^2&=30
\end{align}