The sketch shows circle C C\,C with centre P(6.5,7)P(6.5, 7)P(6.5,7). The line l l\,l with equation y=12x\displaystyle y = \frac{1}{2}xy=21x is a tangent to C C\,C at point Q(8,4)Q(8, 4)Q(8,4).
Find an equation for CCC.
The line with equation y=12x+k\displaystyle y = \frac{1}{2}x + ky=21x+k, where k k\,k is a non-zero constant, is also a tangent to CCC. Find the value of kkk.
Practise Edexcel A Level Maths Circles with exam-style questions for A 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 A Level Maths (9MA0) 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.
