The curve C C\,C has the equation y=2x+kx∈R,x≠0\displaystyle y = \frac{2}{x} + k \quad x \in \mathbb{R}, x \neq 0y=x2+kx∈R,x=0
The line L L\,L has the equation y=−3x+4y = -3x + 4y=−3x+4
Show that the xxx-coordinate of any point of intersection of L L\,L with C C\,C is given by a solution of the equation
3x2+(k−4)x+2=0 3x^2 + (k - 4)x + 2 = 0 3x2+(k−4)x+2=0Hence find the exact values of k k\,k for which L L\,L is a tangent of CCC.
Hence find the exact coordinates of the point of contact for each value of k k\,k found in part (b).
211 exam-style questions on Edexcel A Level Maths Quadratics, covering 2.1 Solving Quadratics, 2.2 Completing the Square, 2.3 Sketching Quadratic Graphs, 2.4 The Discriminant, and 2.5 Modelling with Quadratics. Each one has a worked solution and a mark scheme showing where the marks go.