Question

How do you graph `x^2 + y^2 = 81`?

Answer 1

It is an equation of a circle with centre at `(0,0)` and radius `9`.

Explanation:

The equation is of the form of a circle with center at origin, as in the general form of a quadratic equation

`ax^2+2hxy+by^2+2fx+2gy+c=0`, while coefficients of `x^2` and `y^2` are equal (i.e. `a=b`), `f, g, h` are all zeros. In fact equation `x^2+y^2=81` graph{x^2+y^2=81 [-20, 20, -10, 10]} can be written as

`(x-0)^2+(y-0)^2=9^2`

and hence it is an equation of a circle with centre at `(0,0)` and radius `9`.

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`.

Since we have no `h` or `k` term, we know that we are centered at the origin.

From `sqrt81`, we know that our radius is `9`. Now we can graph!

graph{x^2+y^2=81 [-20, 20, -10, 10]}

Hope this helps!