2025 IGCSE Additional Mathematics May/June 0606/13 Q5

Solutions by accurate drawing will not be accepted.

A circle, \(C\), has equation \((x-5)^2+(y-12)^2=100\).

1. Find the equation of the tangent to \(C\) at the point \((11,4)\).
   Give your answer in the form \(ax+by=c\), where \(a\), \(b\) and \(c\) are integers.[4]
2. Show that \(C\) and the circle with equation \(x^2+y^2=4\) do not intersect.[2]