Question

What is the radius of the circle whose equation is x2 + y2 = 8?

Answer 1

if that is x^2+y^2=8
then the radius is 2
`√(2)`

Answer 2

The radius of the circle whose equation is
`x^(2)+y^(2)=8` is
`2√(2)`

Explanation:

The equation of a circle centered at the origin
`(0,0)` and radius
`R` is :

`x^(2)+y^(2)=R^(2)` (I)

Where ''
`R`'' is a real number.

For the equation given, we know that

`R^(2)=8` ⇒

`R=√(8)`

`R=√((2).(4))`

`R=2√(2)`

We found out that the radius of the circle is
`R=2√(2)`

For another circle, for example centered at the point
`(a,b)` and radius
`R` the equation is :

`(x-a)^(2)+(y-b)^(2)=R^(2)` (II)

Notice that if we replace the point
`(a,b)` by
`(0,0)` ⇒

`(x-0)^(2)+(y-0)^(2)=R^(2)` ⇒

`x^(2)+y^(2)=R^(2)`

We obtain the equation (I).