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