Determine the equation of this circle. (Show work)?

Question

Tangent to both axes, radius 8 and center lies quadrant IV...
The answer is (x-8)^2 + (y +8)^2 = 64

I just dunno how to get this asnwer so could somone explain or show their work...thanks.

Answer 1

center = ( 8, -8)
and radius is 8
so eq is:
(x-8)^2 + (y +8)^2 = 64

Answer 2

If the radius is 8, then you know the right side is 8^2 = 64.

If the circle is tangent to both axes, then use the fact that at any point on a circle, the tangent line is perpendicular to the radius.

So.....draw a circle in the fourth quadrant that is tangent to the two axes. Now draw a radius from the center up to the x-axis, meeting the axis perpendicularly. You know the radius has length 8, so that means the center is 8 units below the x-axis. thus the center has y coordinate -8.

Likewise draw a radius from the center to the y=axis. You know the radius has length 8, so the x-coordinate is positive 8.