MHB Finding the Equation of a Tangent Circle with Center (3,5)

[mathdad]

Find the equation of the circle tangent to the x-axis and with center (3,5).

Can someone get me started? I know this circle touches the line y = 0 and its center point (3,5) lies in quadrant 1.

 

[MarkFL]

Begin by plotting the point (3,5)...now given the circle is tangent to the $x$-axis, what must the radius be?

 

[mathdad]

Begin by plotting the point (3,5)...now given the circle is tangent to the $x$-axis, what must the radius be?

If the center is the point (3,5), this means the y-coordinate represents the distance from the line y = 0 to y = 5.

So, the radius is 5.

I then decided to plug the given point and radius 5 into
(x - h)^2 + (y - k)^2 = r^2.

(x - 3)^2 + (y - 5)^2 = (5)^2

The equation must be (x - 3)^2 + (y - 5)^2 = 25.