The circle C C\,C has the equation x2+y2+8x−4y+k=0x^2 + y^2 + 8x - 4y + k = 0x2+y2+8x−4y+k=0 where k k\,k is a constant. Given that the point (1,5)(1, 5)(1,5) lies on CCC.
Find the value of kkk.
Find the coordinates of the centre and the radius of CCC.
A straight line that passes through the point A(3,7)A(3, 7)A(3,7) is a tangent to the circle C C\,C at the point BBB. Find the exact length of the line ABABAB.
Practise Edexcel AS Level Maths Circles with exam-style questions for AS Level Maths. 28 questions 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, matched to the Edexcel AS Level Maths (8MA0) specification and written in Paper 1 and Paper 2 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.