Where do this pair of tangents to a circle meet?

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The straight line \(x = 3\) intersects the circle \[ x^2 + y^2 - 8x - 10y - 9 = 0 \] at the points \(P\) and \(Q\).

Calculate

1. the coordinates of \(P\) and \(Q\),
2. the equations of the tangents at \(P\) and \(Q\),
3. the coordinates of the point of intersection of the tangents.