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.
178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.