Answer:
Option B - x-axis.
Step-by-step explanation:
Given : Equation [tex]x^2+4y^2=36[/tex]
To find : The major axis runs along?
Solution :
The given equation is an ellipse the general form of an ellipse is
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
Converting into general form of an ellipse,
[tex]x^2+4y^2=36[/tex]
Divide by 36 both side,
[tex]\frac{x^2}{36}+\frac{4y^2}{36}=\frac{36}{36}[/tex]
[tex]\frac{x^2}{36}+\frac{y^2}{9}=1[/tex]
[tex]\frac{x^2}{6^2}+\frac{y^2}{3^2}=1[/tex]
Here, a=6 and b=3
Since, a>b then the major axis of the ellipse is parallel to the x-axis.
Therefore, The major axis runs along x-axis of the equation [tex]x^2+4y^2=36[/tex]
So, Option B is correct.
