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 (0,0), vertex at (9,0), and focus at (1,0). The distance from the center to the vertex is the semi-major axis, a = 9. The distance from the center to the focus is c = 1. Using the relationship 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 $\frac { x ^ { 2 } } { 80 } + \frac { y ^ { 2 } } { 81 } = 1$