The line \(x - y = 4\) is a chord of the circle \((x - 4)^2 + (y + 3)^2 = 9\), which cuts the circle at points Q & R. If \(P(\alpha, \beta)\) lies on the circle such that \(PQ = PR\), then find \((6\alpha + 8\beta)^2\).
Show Hint
The condition $PQ=PR$ for points on a circle implies that $P$ lies on the diameter perpendicular to $QR$. Finding the equation of this diameter is much faster than solving for $Q$ and $R$ coordinates.