Find the standard form of the equation of the ellipse with the given characteristics.
Vertices: $( 0,4 ) , ( 8,4 )$ ;minor axis of length 10.

A) $\frac { ( x + 4 ) ^ { 2 } } { 16 } + \frac { ( y + 4 ) ^ { 2 } } { 25 } = 1$
B) $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$
C) $\frac { ( x + 4 ) ^ { 2 } } { 16 } + \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$
D) $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y + 4 ) ^ { 2 } } { 25 } = 1$
E) $\frac { ( x - 4 ) ^ { 2 } } { 16 } - \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$

Question

Find the standard form of the equation of the ellipse with the given characteristics. ​
Vertices: $( 0,4 ) , ( 8,4 )$ ;minor axis of length 10.
​
A) $\frac { ( x + 4 ) ^ { 2 } } { 16 } + \frac { ( y + 4 ) ^ { 2 } } { 25 } = 1$
B) $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$
C) $\frac { ( x + 4 ) ^ { 2 } } { 16 } + \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$
D) $\frac { ( x - 4 ) ^ { 2 } } { 16 } + \frac { ( y + 4 ) ^ { 2 } } { 25 } = 1$
E) $\frac { ( x - 4 ) ^ { 2 } } { 16 } - \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$

Quizplus · Accepted Answer

The vertices at $(0,4)$ and $(8,4)$ indicate the major axis is horizontal, centered at $(4,4)$, with a length of 8, so $a=4$ and $a^2=16$. The minor axis length is 10, so $b=5$ and $b^2=25$. The correct equation is $\frac{(x-4)^2}{16} + \frac{(y-4)^2}{25} = 1$.

Find the Standard Form of the Equation of the Ellipse (0,4),(8,4)( 0,4 ) , ( 8,4 )(0,4),(8,4)

Find the Standard Form of the Equation of the Ellipse $( 0,4 ) , ( 8,4 )$