(a) Consider the circle that has its center at the point (2, -3) and passes through the point (5, -1). Find the radius of this circle, and find the point-slope and slope-intercept forms of the equation of the line which is tangent to this circle at the point (5, -1). In your solution, use only algebra and the fact that a line which is tangent to a circle is perpendicular to the line that passes through the center of the circle and the point of tangency.
(b) Do the same for a circle that has its center at the point (h, k) and passes through the point (x_0, y_0), where h, k, x_0, y_0 are real numbers such that the conditions h = x_0 and k = y_0 are not both satisfied.
(c) In part (b) above, why do we specify that the conditions h = x_0 and k = y_0 are not both satisfied?