Edexcel C1 — Question 16

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
TopicCircles

16. \section*{Figure 3}
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The points \(A ( - 3 , - 2 )\) and \(B ( 8,4 )\) are at the ends of a diameter of the circle shown in Fig. 3.
  1. Find the coordinates of the centre of the circle.
  2. Find an equation of the diameter \(A B\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.
  3. Find an equation of tangent to the circle at \(B\). The line \(l\) passes through \(A\) and the origin.
  4. Find the coordinates of the point at which \(l\) intersects the tangent to the circle at \(B\), giving your answer as exact fractions.