Edexcel C2 2005 June — Question 8

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2005
SessionJune
TopicCircles

8. The circle \(C\), with centre at the point \(A\), has equation \(x ^ { 2 } + y ^ { 2 } - 10 x + 9 = 0\). Find
  1. the coordinates of \(A\),
  2. the radius of \(C\),
  3. the coordinates of the points at which \(C\) crosses the \(x\)-axis. Given that the line \(l\) with gradient \(\frac { 7 } { 2 }\) is a tangent to \(C\), and that \(l\) touches \(C\) at the point \(T\),
  4. find an equation of the line which passes through \(A\) and \(T\).