Answer:
The equation of the sphere with center (-2, 3, 7) and radius 7 is [tex](x+2)^{2}+(y-3)^{2}+(z-7)^{2} = 49[/tex].
The intersection of the sphere with the yz-plane is [tex](y-3)^{2}+(z-7)^{2} = 49[/tex].
Step-by-step explanation:
We know that any sphere can be represented by the following equation:
[tex](x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}[/tex]
Where:
[tex]h[/tex], [tex]k[/tex], [tex]s[/tex] - Coordinates of the center of the sphere, dimensionless.
[tex]r[/tex] - Radius of the sphere, dimensionless.
If [tex](h,k, s) = (-2,3,7)[/tex] and [tex]r = 7[/tex], we obtain this expression:
[tex](x+2)^{2}+(y-3)^{2}+(z-7)^{2} = 49[/tex]
The intersection of the sphere with the yz-plane observe the following conditions:
[tex]x = 0[/tex], [tex]y \in \mathbb {R}[/tex], [tex]z\in \mathbb{R}[/tex]
Hence, the expression above can be reduced into this:
[tex](y-3)^{2}+(z-7)^{2} = 49[/tex]
