Find the standard form of the equation of the ellipse with the given characteristics.
Foci: $( 5,3 ) , ( 5,13 )$ , endpoints of the major axis: $( 5,0 ) , ( 5,16 )$
A) $\frac { ( x + 8 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 39 } = 1$
B) $\frac { ( x + 5 ) ^ { 2 } } { 64 } + \frac { ( y - 8 ) ^ { 2 } } { 39 } = 1$
C) $\frac { ( x - 5 ) ^ { 2 } } { 39 } + \frac { ( y + 8 ) ^ { 2 } } { 64 } = 1$
D) $\frac { ( x + 5 ) ^ { 2 } } { 39 } + \frac { ( y - 8 ) ^ { 2 } } { 64 } = 1$
E) $\frac { ( x - 8 ) ^ { 2 } } { 64 } + \frac { ( y + 5 ) ^ { 2 } } { 39 } = 1$

Question

Find the standard form of the equation of the ellipse with the given characteristics. 
Foci: $( 5,3 ) , ( 5,13 )$ , endpoints of the major axis: $( 5,0 ) , ( 5,16 )$ 
A) $\frac { ( x + 8 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 39 } = 1$
B) $\frac { ( x + 5 ) ^ { 2 } } { 64 } + \frac { ( y - 8 ) ^ { 2 } } { 39 } = 1$
C) $\frac { ( x - 5 ) ^ { 2 } } { 39 } + \frac { ( y + 8 ) ^ { 2 } } { 64 } = 1$
D) $\frac { ( x + 5 ) ^ { 2 } } { 39 } + \frac { ( y - 8 ) ^ { 2 } } { 64 } = 1$
E) $\frac { ( x - 8 ) ^ { 2 } } { 64 } + \frac { ( y + 5 ) ^ { 2 } } { 39 } = 1$

Quizplus · Accepted Answer

The center of the ellipse is at (5,8), the major axis is vertical with length 16, so $a^2 = 64$. The distance between the foci is 10, so $c = 5$. Using $c^2 = a^2 - b^2$, we find $b^2 = 39$. The equation is $\frac{(x-5)^2}{39} + \frac{(y-8)^2}{64} = 1$.

Find the Standard Form of the Equation of the Ellipse (5,3),(5,13)( 5,3 ) , ( 5,13 )(5,3),(5,13)

Find the Standard Form of the Equation of the Ellipse $( 5,3 ) , ( 5,13 )$