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

idk wish i did Step-by-step explanation:...

What type of conic section is given by the equation

amadileaks

01.01.2022

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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