AQA C1 2006 January — Question 5

Exam BoardAQA
ModuleC1 (Core Mathematics 1)
Year2006
SessionJanuary
TopicCircles

5 A circle with centre \(C\) has equation \(x ^ { 2 } + y ^ { 2 } - 8 x + 6 y = 11\).
  1. By completing the square, express this equation in the form $$( x - a ) ^ { 2 } + ( y - b ) ^ { 2 } = r ^ { 2 }$$
  2. Write down:
    1. the coordinates of \(C\);
    2. the radius of the circle.
  3. The point \(O\) has coordinates \(( 0,0 )\).
    1. Find the length of CO .
    2. Hence determine whether the point \(O\) lies inside or outside the circle, giving a reason for your answer.