SPS SPS SM 2025 October — Question 13

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2025
SessionOctober
TopicCircles

13. The circle \(C\) has equation $$x ^ { 2 } + y ^ { 2 } + 10 x - 4 y + 1 = 0$$
  1. Find
    1. the coordinates of the centre of \(C\)
    2. the exact radius of \(C\) The line with equation \(y = k\), where \(k\) is a constant, cuts \(C\) at two distinct points.
  2. Find the range of values for \(k\), giving your answer in set notation.
  3. The line with equation \(y = m x + 4\) is a tangent to C . Find possible exact values of m .
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