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.
