I am trying to map this equation of a circle and I am wondering if it is right.

A circle whose equation is (x-2)^2 + (y+1)^2 = 8 is translated as four unitds right and three units down. Write the equation of the new circle. Write the mapping rule that maps the unit circle to the new circle.

So I came up with this:

(x-6)^2 + (y+4)^2= Square root of 8^2 for the equation

and (x,y) --> (x + 6, y - 4) for the mapping.

Is this right?