Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

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

Sagot :

Ryan2
[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}
lublana

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]

View image lublana
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.