Find an equation for the ellipse described.
-Center $( 0,0 )$; major axis vertical with length 14 ; length of minor axis is 8
A) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 25 } = 1$
B) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$
C) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 196 } = 1$
D) $\frac { x ^ { 2 } } { 10 } + \frac { y ^ { 2 } } { 49 } = 1$

Question

Quizplus · Accepted Answer

The lengths of the major and minor axes are given as 14 and 8, respectively. Since the major axis is vertical, its length corresponds to the distance along the y-axis, and the minor axis corresponds to the distance along the x-axis. The semi-major axis length (a) is half of 14, which is 7, and the semi-minor axis length (b) is half of 8, which is 4. The standard form of an ellipse's equation 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. Therefore, the equation becomes $\frac{x^2}{4^2} + \frac{y^2}{7^2} = 1$, which simplifies to $\frac{x^2}{16} + \frac{y^2}{49} = 1$.

Find an Equation for the Ellipse Described (0,0)( 0,0 )(0,0) ; Major Axis Vertical with Length 14 ; Length of )

Find an Equation for the Ellipse Described $( 0,0 )$ ; Major Axis Vertical with Length 14 ; Length of )