The points A(3,a)A(3, a)A(3,a) and B(12,7)B(12, 7)B(12,7) lie on a circle. AB AB\,AB is a diameter of the circle. The circle has equation (x−7.5)2+(y−5.5)2=22.5(x - 7.5)^2 + (y - 5.5)^2 = 22.5(x−7.5)2+(y−5.5)2=22.5.
Find the value of a a\,a and the gradient of ABABAB.
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.