Problem:A circle A passing through the point (4, 0) is orthogonal to a circle B with equation x^2+y^2=4. Show that the locus of the centre of the circle A is a straight line and find its equation.

Well, I first established the centre and radius of circle B as (0, 0) and 2 respectively. Then, I let the centre of circle A be (a,b). Then, I reasoned that since circles are orhtogonal, the square of the distance between the centre should be equal to the sum of the squares of the two radii, so that:a^2+b^2 = 4 + (0-a)^2 + (4-b)^2. This gave me the value ofabut then I got stuck. Was I on the right track? Any suggestions please?

Thanks in advance