Edexcel F3 2015 June — Question 5

Exam BoardEdexcel
ModuleF3 (Further Pure Mathematics 3)
Year2015
SessionJune
TopicConic sections

  1. The ellipse \(E\) has equation \(\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1\)
The line \(L\) has equation \(y = m x + c\), where \(m\) and \(c\) are constants.
Given that \(L\) is a tangent to \(E\),
  1. show that $$c ^ { 2 } - 25 m ^ { 2 } = 9$$
  2. find the equations of the tangents to \(E\) which pass through the point \(( 3,4 )\).