Question

A particular circle in the standard (x,y) coordinate

plane has an equation of (x − 5)2 + y2 = 38. What are
the radius of the circle, in coordinate units, and the
coordinates of the center of the circle?

Answer 1

For any circle with Cartesian equation

`(x-a)^2 + (y-b)^2 = r^2`,
we have that the centre of the circle is
`(a,b)`, and the radius of the circle is
`r`.

So in the case that

`(x-5)^2 + y^2 = 38`,
we essentially have that

`a = 5, b = 0, r^2 = 38`.

So the centre of the circle is
`(5,0)`, and the radius is
`√(38)`.