Determine the length of the major and minor axis.
-$$4 x ^ { 2 } + 81 y ^ { 2 } = 324$$
A) length of major axis: 18 ;
length of minor axis: 4
B) length of major axis: 81 ;
length of minor axis: 4
C) length of major axis: 2 ;
length of minor axis: 9
D) length of major axis: 9 ;
length of minor axis: 2

Question

Determine the length of the major and minor axis.
-$$4 x ^ { 2 } + 81 y ^ { 2 } = 324$$
A) length of major axis: 18 ;
 length of minor axis: 4 
B) length of major axis: 81 ;
length of minor axis: 4
C) length of major axis: 2 ;
length of minor axis: 9
D) length of major axis: 9 ; 
 length of minor axis: 2

Quizplus · Accepted Answer

The given equation is of an ellipse in the standard form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $a^2$ and $b^2$ are the denominators under $x^2$ and $y^2$ respectively. To get it in standard form, divide the entire equation by 324: $\frac{4x^2}{324} + \frac{81y^2}{324} = 1$, simplifying to $\frac{x^2}{81} + \frac{y^2}{4} = 1$. Here, $a^2 = 81$ and $b^2 = 4$, so $a = 9$ and $b = 2$. The length of the major axis is $2a = 18$ and the length of the minor axis is $2b = 4$.

Determine the Length of the Major and Minor Axis 4x2+81y2=3244 x ^ { 2 } + 81 y ^ { 2 } = 3244x2+81y2=324

Determine the Length of the Major and Minor Axis $4 x ^ { 2 } + 81 y ^ { 2 } = 324$