Describe the Given Set of Points with a Single Equation $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 225$

Multiple Choice

Describe the given set of points with a single equation or with a pair of equations.
-The circle in which the plane through the point (-8, 12, ) perpendicular to the y-axis meets the sphere of radius 15 centered at the origin.

A) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 225$ and $y = 12$
B) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 81$ and $y = 12$
C) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 63$ and $y = 12$
D) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 144$ and $y = 12$