OCR C1 — Question 6

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
TopicCircles

6. The points \(P\) and \(Q\) have coordinates \(( - 2,6 )\) and \(( 4 , - 1 )\) respectively. Given that \(P Q\) is a diameter of circle \(C\),
  1. find the coordinates of the centre of \(C\),
  2. show that \(C\) has the equation $$x ^ { 2 } + y ^ { 2 } - 2 x - 5 y - 14 = 0$$ The point \(R\) has coordinates (2, 7).
  3. Show that \(R\) lies on \(C\) and hence, state the size of \(\angle P R Q\) in degrees.