Question

How do you graph `x^2 + y^2 = 16`?

Answer 1

This is a circle of radius `4` centred at the origin.

Explanation:

Given:

`x^2+y^2=16`

Note that we can rewrite this equation as:

`(x-0)^2+(y-0)^2 = 4^2`

This is in the standard form:

`(x-h)^2+(y-k)^2 = r^2`

of a circle with centre `(h, k) = (0, 0)` and radius `r = 4`

So this is a circle of radius `4` centred at the origin:

graph{x^2+y^2 = 16 [-10, 10, -5, 5]}

Answer 2

See below:

Explanation:

The equation of a circle is given by

`(x-h)^2+(y-k)^2=r^2`

With center `(h,k)` and radius `r`.

We have no `h` or `k` term, so we know our circle is centered at the origin.

We know from `sqrt16` that our radius is `4`. Now, we have everything we need to graph!

graph{x^2+y^2=16 [-10, 10, -5, 5]}

Hope this helps!