Edexcel FP3 2013 June — Question 1

Exam BoardEdexcel
ModuleFP3 (Further Pure Mathematics 3)
Year2013
SessionJune
TopicConic sections

  1. A hyperbola \(H\) has equation
$$\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { 25 } = 1 , \quad \text { where } a \text { is a positive constant. }$$ The foci of \(H\) are at the points with coordinates \(( 13,0 )\) and \(( - 13,0 )\).
Find
  1. the value of the constant \(a\),
  2. the equations of the directrices of \(H\).