The equation x2+y2−4x+6y−12=0 represents a circle. Answer the questions that follow.
a. (i) Rewrite the equation in standard form and hence determine the centre and the radius of the circle.
b. (ii) Find the points where the circle intersects the x-axis and the y-axis, giving exact coordinates.
c. (iii) Sketch the circle on graph paper, showing the centre, radius, and all intercepts obtained in part (ii).