A circle C C\,C has centre (10,6)(10, 6)(10,6) and radius 2k2\sqrt{k}2k, where 0<k<250<k<250<k<25. A line L L\,L has equation y=mxy=mxy=mx.
Show that the xxx-coordinate of any points of intersection of C C\,C and L L\,L satisfies the equation (m2+1)x2−(12m+20)x+136−4k=0(m^2+1)x^2-(12m+20)x+136-4k=0(m2+1)x2−(12m+20)x+136−4k=0.
Find values of m m\,m for which the equation in (a) has equal roots, giving your answers in terms of kkk.
Two lines drawn from the origin which are tangents to CCC. Find the coordinates of the points of contact between the tangents and C C\,C in terms of kkk.
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.