Write the standard form of the equation of the ellipse centered at the origin, having a vertical 20 units and a minor axis of 10 units.
A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 100 } = 1$
B) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 25 } = 1$
C) $\frac { x ^ { 2 } } { 50 } + \frac { y ^ { 2 } } { 200 } = 1$
D) $\frac { x ^ { 2 } } { 20 } + \frac { y ^ { 2 } } { 10 } = 1$
E) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 400 } = 1$

Question

Quizplus · Accepted Answer

The standard form of the equation of an ellipse centered at the origin is $\frac { x ^ { 2 } } { b ^ { 2 } } + \frac { y ^ { 2 } } { a ^ { 2 } } = 1$, where $a$ is the length of the semi-major axis and $b$ is the length of the semi-minor axis. In this case, the semi-major axis is 20 units and the semi-minor axis is 10 units, so the equation of the ellipse is $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 100 } = 1$.

Write the Standard Form of the Equation of the Ellipse x225+y2100=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 100 } = 125x2​+100y2​=1

Write the Standard Form of the Equation of the Ellipse $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 100 } = 1$