Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. ( x² + y² + (z - 12)¹² = 225, z = 0 )
a) A sphere centered at the origin with radius 15, intersecting the xy-plane at ( z = 12 )
b) A cone along the z-axis with base radius 15 and apex at ( z = 12 )
c) A cylinder along the z-axis with radius 15 and centered at ( z = 12 )
d) A plane intersecting the xy-plane at ( z = 12 ) and forming a circle of radius 15