B) there is a line with positive slope that is tangent to both circles. find the equation of this line, and (c) determine the points at which this tangent line touches each circle

Given that there is a line with positive slope that is tangent to both circles and .

Let the point of tangency in the first circle be (a, b) and the point of tangency in the second circle be (c, d), then the slope of the tangent to the first circle is given by



and the slope of the second circle is given by



From the first circle equation, we have



and from the second equation, we have



Since the two slopes above are for the same line, then



Thus, we have