Here is one solution to (d). Let's lower the circle by 1 so that the center is at (0, 0). Suppose the middle of a chord LM has coordinates (x0, y0). Then the line from (0, 0) to (x0, y0) is perpendicular to LM, so the line LM has the equation xx0 + yy0 = c for some constant c. (If this is unclear, please say so.) Since (x0, y0) ∈ LM, . Now, since (0, -4) ∈ line LM, . This is the required equation in x0 and y0, only the locus has to lifted back up by 1.