The points DDD, E E\,E and F F\,F have coordinates (4,k)(4, k)(4,k), (4,−1)(4, -1)(4,−1) and (1,−1)(1, -1)(1,−1) respectively, where k k\,k is a constant and k≠−1k\ne-1k=−1.
Show that angle DEF DEF\,DEF is a right angle.
Given that DDD, E E\,E and F F\,F all lie on the circle CCC, find, in terms of kkk, the coordinates of the centre of CCC.
Find, in terms of kkk, the equation of the circle 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.