Find the Equation of the Ellipse with Center At $( 8,9 )$

Multiple Choice

Find the equation of the ellipse with center at $( 8,9 )$ , vertex at $( 16,9 )$ , and passing through the intersection of $y = - 2 x + 27$ and $y = x + 3$ .

A) $\frac { ( x - 8 ) ^ { 2 } } { 8 } + \frac { ( y - 9 ) ^ { 2 } } { 2 } = 1$
B) $\frac { ( x - 8 ) ^ { 2 } } { 49 } + \frac { ( y - 9 ) ^ { 2 } } { 9 } = 1$
C) $\frac { ( x - 8 ) ^ { 2 } } { 64 } + \frac { ( y - 9 ) ^ { 2 } } { 4 } = 1$
D) $\frac { ( x - 8 ) ^ { 2 } } { 49 } + \frac { ( y - 9 ) ^ { 2 } } { 4 } = 1$
E) $\frac { ( x - 8 ) ^ { 2 } } { 81 } + \frac { ( y - 9 ) ^ { 2 } } { 9 } = 1$