The circle C C\,C has the equation x2+y2+8x−2y+k=0x^2 + y^2 + 8x - 2y + k = 0x2+y2+8x−2y+k=0 where k k\,k is a constant. Given that the point (1,5)(1, 5)(1,5) lies on CCC.
A straight line that passes through the point A(3,8)A(3, 8)A(3,8) is a 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.