Consider the circle x2+y2−6x+4y−12=0.
(i) Convert the given equation to its standard form and hence find the centre and radius of the circle.
(ii) Using an algebraic test, decide the relative positions of the points A(3,2) and B(−1,1) with respect to the circle.
(iii) Find all real values of k for which the point P(k,1) lies strictly inside the circle.