10.
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The diagram shows the curve \(y = x ^ { 2 } - 3 x + 5\) and the straight line \(y = 2 x + 1\). The curve and line intersect at the points \(P\) and \(Q\).
- Using algebra, show that \(P\) has coordinates \(( 1,3 )\) and find the coordinates of \(Q\).
- Find an equation for the tangent to the curve at \(P\).
- Show that the tangent to the curve at \(Q\) has the equation \(y = 5 x - 11\).
- Find the coordinates of the point where the tangent to the curve at \(P\) intersects the tangent to the curve at \(Q\).