The circle C C\,C has centre (4,k)(4, k)(4,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(2,3)A(2, 3)A(2,3).
Show that the gradient of the radius AC AC\,AC is −12\displaystyle -\frac{1}{2}−21.
Find an equation for CCC.
292 exam-style questions on Edexcel A Level Maths Circles, 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. Each one has a worked solution and a mark scheme showing where the marks go.