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.
178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.