QUESIION 10.4
Writing the Equation of a Sphere Given its Center and Radius
Choose one $\cdot 5$ points
Write the equation of a sphere with center $\vec{c}=(3,2,1)$ and radius $R=5$
\[
\begin{array}{l}
(x-3)^{2}+(y-2)^{2}+(z-1)^{2}=25 \\
(x-3)^{2}+(y-2)^{2}+(z-1)^{2}=5 \\
(x+3)^{2}+(y+2)^{2}+(z+1)^{2}=5
\end{array}
\]
Answer
\(\boxed{(x-3)^{2}+(y-2)^{2}+(z-1)^{2}=25}\)
Step 1 ：The equation of a sphere in 3D space is given by \((x-a)^2 + (y-b)^2 + (z-c)^2 = r^2\), where \((a, b, c)\) is the center of the sphere and \(r\) is the radius.
Step 2 ：In this case, the center of the sphere is given as \((3, 2, 1)\) and the radius is \(5\).
Step 3 ：We can substitute these values into the equation to get the equation of the sphere.
Step 4 ：The equation of the sphere is \((x-3)^{2}+(y-2)^{2}+(z-1)^{2}=25\)
Step 5 ：\(\boxed{(x-3)^{2}+(y-2)^{2}+(z-1)^{2}=25}\)
