Edexcel FP2 Specimen — Question 6

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
SessionSpecimen
TopicComplex Numbers Argand & Loci

  1. A curve has equation
$$| z + 6 | = 2 | z - 6 | \quad z \in \mathbb { C }$$
  1. Show that the curve is a circle with equation \(x ^ { 2 } + y ^ { 2 } - 20 x + 36 = 0\)
  2. Sketch the curve on an Argand diagram. The line \(l\) has equation \(a z ^ { * } + a ^ { * } z = 0\), where \(a \in \mathbb { C }\) and \(z \in \mathbb { C }\)
    Given that the line \(l\) is a tangent to the curve and that \(\arg a = \theta\)
  3. find the possible values of \(\tan \theta\)