- The circle \(C\) has equation
$$( x - 3 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 30$$
Write down
- the coordinates of the centre of \(C\),
- the exact value of the radius of \(C\).
Given that the point \(P\) with coordinates \(( 6 , k )\), where \(k\) is a constant, lies inside circle \(C\), (b) show that
$$k ^ { 2 } + 8 k - 5 < 0$$
- Hence find the exact set of values of \(k\) for which \(P\) lies inside \(C\).
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