The circle C C\,C has the equation
x2+y2+6x−2y+k=0, x^2+y^2+6x-2y+k=0, x2+y2+6x−2y+k=0,where k k\,k is a constant. Given that the point (2,4)(2,4)(2,4) lies on CCC.
A straight line that passes through the point A(6,8)A(6,8)A(6,8) is tangent to the circle C C\,C at the point BBB.
Find the value of kkk, the coordinates of the centre and the radius of CCC, and the exact length of the line 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.