Question

Graph 4x2+4y2=64. What are the domain and range?

Answer 1

EXPLANATION

The given equation is

`4 {x}^(2) + 4 {y}^(2) = 64`

We divide through by 4 to obtain;

`{x}^(2) + {y}^(2) = 16`

This can again be written as:

`{x}^(2) + {y}^(2) = {4}^(2)`

This is the equation of a circle centered at the origin with radius 4 units.

The graph is shown in the attachment.

Answer 2

Domain: [-4,4]

Range : [-4,4]

Explanation:

Given equation is
`4x^2+4y^2=64`.

Now we need to graph and find about what are domain and range of the given problem.

`4x^2+4y^2=64`

divide both sides by 4

`x^2+y^2=16`

`x^2+y^2=4^2`

Which looks similar to the formula of circle

`x^2+y^2=r^2`

that means it is a circle with radius 4. whose centre is at the origin.

From graph we can easily see that

Domain: [-4,4]

Range : [-4,4]