Write the standard form of the equation of the ellipse centered at the origin, having a horizontal major axis of 6 units and a minor axis of 4 units.
A) $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 4 } = 1$
B) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$
C) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 36 } = 1$
D) $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 18 } = 1$
E) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

Question

Quizplus · Accepted Answer

The standard form of the equation of an ellipse centered at the origin with a horizontal major axis is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $2a$ is the length of the major axis and $2b$ is the length of the minor axis. Given a major axis of 6 units and a minor axis of 4 units, $a = 3$ and $b = 2$, so the equation becomes $\frac{x^2}{9} + \frac{y^2}{4} = 1$.

Write the Standard Form of the Equation of the Ellipse x26+y24=1\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 4 } = 16x2​+4y2​=1

Write the Standard Form of the Equation of the Ellipse $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 4 } = 1$