Write the equation of the ellipse that has its center at the origin, focus at (1, 0) and vertex at (9, 0).
A) $\frac { x ^ { 2 } } { 80 } + \frac { y ^ { 2 } } { 81 } = 1$
B) $\frac { x ^ { 2 } } { 1 } + \frac { y ^ { 2 } } { 9 } = 1$
C) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 80 } = - 1$
D) $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 80 } = 1$
E) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 80 } = 1$

Question

Write the equation of the ellipse that has its center at the origin, focus at (1, 0) and vertex at (9, 0). 
A) $\frac { x ^ { 2 } } { 80 } + \frac { y ^ { 2 } } { 81 } = 1$
B) $\frac { x ^ { 2 } } { 1 } + \frac { y ^ { 2 } } { 9 } = 1$
C) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 80 } = - 1$
D) $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 80 } = 1$
E) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 80 } = 1$

Quizplus · Accepted Answer

The ellipse is horizontal with center at the origin, vertex at (9,0), and focus at (1,0). The distance from the center to the vertex is 9, so $a^2 = 81$. The distance from the center to the focus is 1, so $c = 1$. Using $c^2 = a^2 - b^2$, we find $b^2 = 80$. Thus, the equation is $\frac{x^2}{81} + \frac{y^2}{80} = 1$.

Write the Equation of the Ellipse That Has Its Center x280+y281=1\frac { x ^ { 2 } } { 80 } + \frac { y ^ { 2 } } { 81 } = 180x2​+81y2​=1

Write the Equation of the Ellipse That Has Its Center $\frac { x ^ { 2 } } { 80 } + \frac { y ^ { 2 } } { 81 } = 1$