AQA AS Paper 2 2021 June — Question 11

Exam BoardAQA
ModuleAS Paper 2 (AS Paper 2)
Year2021
SessionJune
TopicCircles

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