2025 IGCSE Additional Mathematics October/November 0606/13 Q11

2025 IGCSE Additional Mathematics October/November 0606/13 Q11

7 marks

The lines \(x=0\), \(x=4\), \(y=3\) and \(y=-1\) are tangents to a circle.

  1. Find the equation of the circle.[3]
    The line \(y=2x+a\), where \(a\) is a constant, is also a tangent to the circle.
  2. Show that \(5x^2+4(a-2)x+(a-1)^2=0\), and hence find the possible values of \(a\).
    Give your answers in exact form.[4]

Solution:

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Answer:(a) \((x-2)^2+(y-1)^2=4\) (b) Shown; \(a=-3\pm2\sqrt5\).

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