5. A curve has the equation \(y = \sqrt { 3 x + 11 }\).
The point \(P\) on the curve has \(x\)-coordinate 3 .
- Show that the tangent to the curve at \(P\) has the equation
$$3 x - 4 \sqrt { 5 } y + 31 = 0$$
The normal to the curve at \(P\) crosses the \(y\)-axis at \(Q\).
- Find the \(y\)-coordinate of \(Q\) in the form \(k \sqrt { 5 }\).