Find the equation of the tangent PQ to the circle at point A.

From the diagram 3.4, the centre of the circle is $O(0, -1)$.
The point where the tangent touches the circle is $A(9, -1)$.

The radius OA connects the centre $O(0, -1)$ and the point of tangency $A(9, -1)$.
The gradient $m_{OA}$ is given by the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Since the gradient of the radius OA is 0, the radius OA is a horizontal line.

The tangent line PQ is perpendicular to the radius OA at the point of tangency A.
If the radius OA is a horizontal line, then the tangent PQ must be a vertical line.
A vertical line passing through a point $(x_1, y_1)$ has the equation $x = x_1$.
The tangent PQ passes through point $A(9, -1)$.
Therefore, the equation of the tangent PQ is $x = 9$.