2025 IGCSE Additional Mathematics May/June 0606/11 Q3

2025 IGCSE Additional Mathematics May/June 0606/11 Q3

6 marks

Point \(A\) has coordinates \((3,-1)\).

A circle has equation \((x-4)^2+(y+3)^2=5\).

  1. Show that \(A\) lies on the circumference of the circle.[1]
  2. Given that \(AB\) is a diameter of the circle, find the coordinates of \(B\).[2]
  3. Find the equation of the tangent to the circle at \(A\).[3]

Solution:

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Answer:(a) \((3-4)^2+(-1+3)^2=5\) (shown) (b) \(B=(5,-5)\) (c) \(y+1=\dfrac12(x-3)\)

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