Question

Find the center and radius of a circle with the equation x^2 + y^2 = 20.

Answer 1

The given equation of the circle is:

`\rm \: x^2 + y^2 = 20`

We can write this equation in standard form by completing the square:

`\rm x^2 + y^2 = 20`

`\rm x^2 + y^2 - 20 = 0`

`\rm (x^2 - 2x + 1) + (y^2 - 20) = 1`

`\rm (x - 1)^2 + y^2 = 21`

Therefore, the center of the circle is (1, 0) and the radius is the square root of 21.