The equation x2+y2−4x+6y−12=0 represents a circle.
a. (i) Rewrite the given equation in standard form by completing the squares.
b. (ii) Using the result of part (i), determine the centre and radius of the circle.
c. (iii) Find the distance of the centre from the origin and state whether the origin lies inside, on, or outside the circle, justifying your answer.