S6.12.11 Find an equation of the sphere

[karush]

$\tiny{s6.12.11}\\$
\begin{align}
&\textsf{(a) Find an equation of the sphere with center (1, -4, 3) and radius 5. }\\
&(x - 1)^2 +( y +4)^2 +(z - 3 )^2 = 5 ^2=25 \\
\\
&\textsf{(b) What is the intersection of this sphere with the
xz-plane?.}\\
&\textit{assume it is an equation of a circle for the intersection}\\
\end{align}
$\textit{}$

 

[MarkFL]

For a sphere of radius $r$ and centered at $(a,b,c)$, we have:

$$(x-a)^2+(y-b)^2+(z-c)^2=r^2$$

What is the value of $y$ for all points in the $xz$-plane?

 

[MarkFL]

In the $xz$-plane, we have $y=0$...:D