Verified Answer :

Ryan2

\(4x^2+9y^2=36\\ \\ \frac{4x^2}{36}+\frac{9y^2}{36}=\frac{36}{36}\\ \\ \boxed{\frac{x^2}{9}+\frac{y^2}{4}=1}\)

This is a equation of a ellipse (0,0) centered

Domais: {x∈R/-3≤x≤3}
Range:{y∈R/-2≤y≤2}

lublana

Answer:

Ellipse

Domain:[-3,3]

Range:[-2,2]

Step-by-step explanation:

We are given that an equation

\(4x^2+9y^2=36\)

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

\(\frac{x^2}{9}+\frac{y^2}{4}=1\)

\(\frac{x^2}{3^2}+\frac{y^2}{2^2}=1\)

It is an equation of ellipse.

Substitute y=0 then , we get

\(\frac{x^2}{9}=1\)

\(x^2=9\)

\(x=\pm 3\)

Domain :[-3,3]

Substitute x=0 then we get

\(\frac{y^2}{4}=1\)

\(y^2=4\)

\(y=\pm 2\)

Range=[-2,2]

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