A circle C C\,C has centre (10,6)(10, 6)(10,6) and radius 2172\sqrt{17}217. 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+68=0(m^2 + 1)x^2 - (12m + 20)x + 68 = 0(m2+1)x2−(12m+20)x+68=0.
Find values of m m\,m for which the equation in (a) has equal roots.
Two lines drawn from the origin which are tangents to CCC. Find the coordinates of the points of contact between the tangents and CCC.
Practise Edexcel A Level Maths Circles with exam-style questions for A Level Maths. 28 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
