The points A(3,a)A(3, a)A(3,a) and B(8,9)B(8, 9)B(8,9) lie on a circle. AB AB\,AB is a diameter of the circle and has a gradient of 35\displaystyle \frac{3}{5}53. 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 value of aaa.
Hence find the values of ccc, d d\,d and eee.
292 exam-style questions on Edexcel A Level Maths Circles, covering 6.1 Midpoints and Perpendicular Bisectors, 6.2 Equation of a Circle, 6.3 Intersections of Straight Lines and Circles, 6.4 Use Tangent and Chord Properties, and 6.5 Circles and Triangles. Each one has a worked solution and a mark scheme showing where the marks go.