Answer:
This is equation of ellipse
Step-by-step explanation:
we are given
[tex]4x^2+9y^2=36[/tex]
We can see that right side is 36
so, we can make right side as 1 by dividing both sides by 36
[tex]\frac{4x^2+9y^2}{36} =\frac{36}{36}[/tex]
[tex]\frac{4x^2+9y^2}{36} =1[/tex]
[tex]\frac{4x^2}{36}+\frac{9y^2}{36} =1[/tex]
we can simplify it
[tex]\frac{x^2}{9}+\frac{y^2}{4} =1[/tex]
we can rewrite it as
[tex]\frac{x^2}{3^2}+\frac{y^2}{2^2} =1[/tex]
now, we can compare it with standard equation of ellipse
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} =1[/tex]
we can see that both equations are similar
so, this is equation of ellipse
