A circle has centre (h,k) and radius r.
(i) Starting from the geometrical definition of a circle, derive its Cartesian equation in terms of h, k and r.
(ii) Let P(x1,y1) be a point on this circle. Obtain the equation of the straight line that touches the circle only at P.
(iii) Explain geometrically why the line obtained in part (ii) is perpendicular to the radius drawn to P.