SPS SPS SM Pure 2021 June — Question 11

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2021
SessionJune
TopicCircles

11.
  1. A circle \(C _ { 1 }\) has equation $$x ^ { 2 } + y ^ { 2 } + 18 x - 2 y + 30 = 0$$ The line \(l\) is the tangent to \(C _ { 1 }\) at the point \(P ( - 5,7 )\).
    Find an equation of \(l\) in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers to be found.
  2. A different circle \(C _ { 2 }\) has equation $$x ^ { 2 } + y ^ { 2 } - 8 x + 12 y + k = 0$$ where \(k\) is a constant.
    Given that \(C _ { 2 }\) lies entirely in the 4th quadrant, find the range of possible values for \(k\).
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