Solve the Problem $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 11 } = 1$

Multiple Choice

Solve the problem.
-The ellipse $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 11 } = 1$ is shifted down 6 units and right 4 units. Find an equation for the new ellipse and find the new vertices.

A) $\frac { ( x + 4 ) ^ { 2 } } { 5 } + \frac { ( y - 6 ) ^ { 2 } } { 11 } = 1$ ; vertices: $( 4 , - 6 \pm \sqrt { 11 } )$
B) $\frac { ( x - 4 ) ^ { 2 } } { 5 } + \frac { ( y + 6 ) ^ { 2 } } { 11 } = 1$ ; vertices: $( 4 \pm \sqrt { 5 } , - 6 )$
C) $\frac { ( x - 4 ) ^ { 2 } } { 5 } + \frac { ( y + 6 ) ^ { 2 } } { 11 } = 1$ ; vertices: $( 4 , - 6 \pm \sqrt { 11 } )$
D) $\frac { ( x - 6 ) ^ { 2 } } { 5 } + \frac { ( y + 4 ) ^ { 2 } } { 11 } = 1$ ; vertices: $( 4 \pm \sqrt { 5 } , - 6 )$