Find the standard form of the equation of the ellipse with the given characteristics.
Foci: $( 0,0 ) , ( 6,0 )$ ;major axis of length 10.

A) $\frac { ( x - 3 ) ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$
B) $\frac { ( x - 3 ) ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$
C) $\frac { ( x + 3 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$
D) $\frac { ( x - 3 ) ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$
E) $\frac { ( x + 3 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Question

Find the standard form of the equation of the ellipse with the given characteristics. ​
Foci: $( 0,0 ) , ( 6,0 )$ ;major axis of length 10.
​
A) $\frac { ( x - 3 ) ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$
B) $\frac { ( x - 3 ) ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$
C) $\frac { ( x + 3 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$
D) $\frac { ( x - 3 ) ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$
E) $\frac { ( x + 3 ) ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Quizplus · Accepted Answer

The center of the ellipse is at the midpoint of the foci, $(3,0)$. The major axis is horizontal with length 10, so $a = 5$. The distance between the foci is 6, so $c = 3$. Using $b^2 = a^2 - c^2$, we find $b^2 = 16$. The equation is $\frac{(x-3)^2}{25} + \frac{y^2}{16} = 1$.

Find the Standard Form of the Equation of the Ellipse (0,0),(6,0)( 0,0 ) , ( 6,0 )(0,0),(6,0)

Find the Standard Form of the Equation of the Ellipse $( 0,0 ) , ( 6,0 )$