4. Let A be the point where the unit circle centred at the origin intersects the positive xaxis, and B the point where this circle intersects the positive yacxis. Suppose that P is a point on the circle between A and B in the rst quadrant, and that P is not at A or B. The line through P tangent to the circle intersects the positive slyaxis at Q and the positive y-axis at R. Suppose tllnat ill/if is the midpoint of QR. Prove that all such points M lie on a curve with equation 2 + 2 = k, for some real number k. 9/" ll