Provide an Appropriate Response $( \mathrm { c } , 0 )$

Multiple Choice

Provide an appropriate response.
-It can be shown that an ellipse with foci $( \mathrm { c } , 0 )$ and $( - \mathrm { c } , 0 )$ where the sum of the distances from any point $( x , y )$ of the ellipse to the two foci is $2 a$ has equation $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { a ^ { 2 } - c ^ { 2 } } = 1$ . Use this result to find an equation of an ellipse with foci $( 3,0 )$ and $( - 3,0 )$ , where the sum of the distances from any point of the ellipse to the two foci is 8 .

A) $\frac { x ^ { 2 } } { - 3 } + \frac { y ^ { 2 } } { 13 } = 1$
B) $x ^ { 2 } + y ^ { 2 } = 64$
C) $\frac { x ^ { 2 } } { - 3 } + \frac { y ^ { 2 } } { 64 } = 1$
D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 7 } = 1$