Find the Equation of the Surface Satisfying the Conditions, and Identify

Multiple Choice

Find the equation of the surface satisfying the conditions, and identify the surface. The set of points equidistant from the point $( 2,4,5 )$ and the plane $y = - 1$ .

A) $10 y = ( x - 2 ) ^ { 2 } + ( z - 5 ) ^ { 2 } + 15$ , an elliptic paraboloid
B) $( x - 2 ) ^ { 2 } + ( y - 4 ) ^ { 2 } + ( z - 5 ) ^ { 2 } - 5 = 0$ , a sphere
C) $10 y = ( x - 2 ) ^ { 2 } + ( z - 5 ) ^ { 2 } + 1 ,$ , a hyperbolic paraboloid
D) $( x - 2 ) ^ { 2 } + ( y - 4 ) ^ { 2 } + ( z - 5 ) ^ { 2 } - 1 = 0$ , a sphere
E) $10 y = ( x - 2 ) ^ { 2 } + ( z - 5 ) ^ { 2 } - 1$ , , a hyperbolic paraboloid