Find an equation for the ellipse described.
-Center at $( 6,4 )$; focus at $( 10,4 )$; vertex at $( 12,4 )$
A) $\frac { ( x + 6 ) ^ { 2 } } { 36 } + \frac { ( y + 4 ) ^ { 2 } } { 20 } = 1$
B) $\frac { ( x - 6 ) ^ { 2 } } { 81 } + \frac { ( y + 4 ) ^ { 2 } } { 8 } = 2$
C) $\frac { ( x + 6 ) ^ { 2 } } { 16 } - \frac { ( y - 4 ) ^ { 2 } } { 16 } = 1$
D) $\frac { ( x - 6 ) ^ { 2 } } { 36 } + \frac { ( y - 4 ) ^ { 2 } } { 20 } = 1$

Question

Quizplus · Accepted Answer

The center of the ellipse is at (6,4), indicating that the equation should be in the form $\frac{(x-6)^2}{a^2} + \frac{(y-4)^2}{b^2} = 1$. The distance from the center to a vertex (a) is 6 units (from (6,4) to (12,4)), so $a^2 = 36$. The distance from the center to a focus (c) is 4 units (from (6,4) to (10,4)), and since $c^2 = a^2 - b^2$, we find $b^2$ by knowing $a^2 = 36$ and $c^2 = 16$, giving $b^2 = 20$.

Find an Equation for the Ellipse Described (6,4)( 6,4 )(6,4) ; Focus At

Find an Equation for the Ellipse Described $( 6,4 )$ ; Focus At