Answer:
Ellipse
Domain:[-3,3]
Range:[-2,2]
Step-by-step explanation:
We are given that an equation
[tex]4x^2+9y^2=36[/tex]
We have to find the type of conic section and find the domain and range of conic section.
Divide by 36 on both sides then, we get
[tex]\frac{x^2}{9}+\frac{y^2}{4}=1[/tex]
[tex]\frac{x^2}{3^2}+\frac{y^2}{2^2}=1[/tex]
It is an equation of ellipse.
Substitute y=0 then , we get
[tex]\frac{x^2}{9}=1[/tex]
[tex]x^2=9[/tex]
[tex]x=\pm 3[/tex]
Domain :[-3,3]
Substitute x=0 then we get
[tex]\frac{y^2}{4}=1[/tex]
[tex]y^2=4[/tex]
[tex]y=\pm 2[/tex]
Range=[-2,2]
