What type of conic section is given by the equation 4x^2+9y^2=36? What are its domain and range?

[tex]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}[/tex]

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

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

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lublana lublana · Answer 2 · 2019-12-19T23:21:21-05:00

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]