MATHEMATICS · Multi-part · A Level · Mathematics · Coordinate geometry in the (x y) plane · Coordinate geometry in the (x y) plane
Problem
The endpoints of a diameter of a circle are A(3,−1) and B(−5,7). Answer the following questions.
(i) Determine the equation of the circle in standard form using the information about the diameter.
(ii) Expand the equation obtained in part (i) to write it in the form x2+y2+2gx+2fy+c=0.
(iii) Starting only with the expanded form obtained in part (ii), recover the centre and radius of the circle. Verify that these values agree with the geometric data of the diameter AB. Show each step clearly.