The endpoints of a diameter of a circle are A(5,−1) and B(−1,3). Using this information, answer the following questions.
(i) Determine the coordinates of the centre of the circle and its radius.
(ii) Obtain the Cartesian equation of the circle in standard form.
(iii) Draw a clear sketch of the circle on a coordinate plane and mark the points where it meets the coordinate axes.
(iv) Verify that the point A lies on the circle by direct substitution in your equation from part (ii).