Question

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

Answer 1

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]

Answer 2

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

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

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