8. The equation \(k \left( 3 x ^ { 2 } + 8 x + 9 \right) = 2 - 6 x\), where \(k\) is a real constant, has no real roots.
- Show that \(k\) satisfies the inequality
$$11 k ^ { 2 } - 30 k - 9 > 0$$
- Find the range of possible values for \(k\).
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\section*{9. In this question you must show detailed reasoning.}
The centre of a circle C is the point \(( - 1,3 )\) and C passes through the point \(( 1 , - 1 )\). The straight line L passes through the points \(( 1,9 )\) and \(( 4,3 )\).
Show that L is a tangent to C .
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