The circle C C\,C has centre (5,k)(5, k)(5,k), where k k\,k is a constant. The line y=2x+1y = 2x + 1y=2x+1 is a tangent to the circle CCC, touching C C\,C at the point A(3,7)A(3, 7)A(3,7).
Find an equation for CCC.
Practise AQA A Level Maths 1.6 C: Coordinate geometry in the (x, y) plane with exam-style questions for A Level Maths. 110 questions covering 1.6.1 Equation of a straight line, 1.6.2 Coordinate geometry of the circle, 1.6.3 Parametric equations of curves (A-level only), and 1.6.4 Parametric equations in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 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.