11 A circle \(C\) has centre \(( 0,10 )\) and radius \(\sqrt { 20 }\)
A line \(L\) has equation \(y = m x\)
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- Show that the \(x\)-coordinate of any point of intersection of \(L\) and \(C\) satisfies the equation
$$\left( 1 + m ^ { 2 } \right) x ^ { 2 } - 20 m x + 80 = 0$$
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- (ii) Find the values of \(m\) for which the equation in part (a)(i) has equal roots.
11 - Two lines are drawn from the origin which are tangents to \(C\).
Find the coordinates of the points of contact between the tangents and \(C\).