Edexcel F3 2023 January — Question 2

Exam BoardEdexcel
ModuleF3 (Further Pure Mathematics 3)
Year2023
SessionJanuary
TopicConic sections

  1. A hyperbola \(H\) has equation
$$\frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { 5 } = 1 \quad \text { where } a \text { is a positive constant }$$ The line with equation \(x = \frac { 4 } { 3 }\) is a directrix of \(H\)
  1. Write down an equation of the other directrix.
  2. Determine
    1. the value of \(a\)
    2. the coordinates of each of the foci of \(H\)