AQA C1 2013 January — Question 7

Exam BoardAQA
ModuleC1 (Core Mathematics 1)
Year2013
SessionJanuary
TopicCircles

7 A circle with centre \(C ( - 3,2 )\) has equation $$x ^ { 2 } + y ^ { 2 } + 6 x - 4 y = 12$$
  1. Find the \(y\)-coordinates of the points where the circle crosses the \(y\)-axis.
  2. Find the radius of the circle.
  3. The point \(P ( 2,5 )\) lies outside the circle.
    1. Find the length of \(C P\), giving your answer in the form \(\sqrt { n }\), where \(n\) is an integer.
    2. The point \(Q\) lies on the circle so that \(P Q\) is a tangent to the circle. Find the length of \(P Q\).