The points A(4,a)A(4, a)A(4,a) and B(13,6)B(13, 6)B(13,6) lie on a circle. AB AB\,AB is a diameter of the circle and has a gradient of 13\displaystyle \frac{1}{3}31. The circle has equation (x−c)2+(y−d)2=e(x - c)^2 + (y - d)^2 = e(x−c)2+(y−d)2=e where ccc, d d\,d and e e\,e are rational numbers.
Find the values of aaa, ccc, d d\,d and eee.
76 exam-style questions on WJEC A Level Maths 1.3 Coordinate geometry in the (x, y) plane, covering 1.3.1 Coordinate geometry in the (x, y) plane, 1.3.2 Coordinate geometry in the (x, y) plane, 1.3.3 Coordinate geometry in the (x, y) plane, and 1.3.4 Coordinate geometry in the (x, y) plane. Each one has a worked solution and a mark scheme showing where the marks go.