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.
143 exam-style questions on OCR A Level Maths 1.3 Coordinate Geometry in the x-y Plane, covering 1.3.1 Straight lines, 1.3.2 Parallel and perpendicular lines, 1.3.3 Straight line models, 1.3.4 Coordinate geometry of a circle, 1.3.5 Centre and radius by completing the square, 1.3.6 Circle properties, 1.3.7 Parametric equations of curves (A-level only), 1.3.8 Parametric equations in context (A-level only), and 1.3 Coordinate Geometry in the x-y Plane. Each one has a worked solution and a mark scheme showing where the marks go.