Answer:
[tex]length\ of \ minor\ axis = 6[/tex]
Step-by-step explanation:
Given:
The given equation is.
[tex]x^{2} +4y^{2} =36[/tex] -------------(1)
We write standard equation of an ellipse
[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2} }{b^{2} } = 1[/tex]-------(2)
So equation 1 divided by 36 for standard form of an equation
[tex]\frac{x^{2}}{36}+\frac{4y^{2} }{36} = \frac{36}{36}[/tex]
[tex]\frac{x^{2}}{36}+\frac{y^{2} }{9} = 1[/tex]
So we compare equation 1 and equation 2.
we get [tex]a^{2} =36[/tex] and [tex]b^{2} =9[/tex]
so [tex]a =6[/tex] and [tex]b =3[/tex]
The length of the minor axis is [tex]2\times b[/tex]
Here [tex]b=3[/tex].
[tex]length\ of \ minor\ axis = 2\times 3[/tex]
[tex]length\ of \ minor\ axis = 6[/tex]
Therefore the length of the minor axis is 6
