\(y^2 = 2x - 3 \) .....(1)
Equation of chord of contact
\(PQ: y.1 = (x + 0) - 3\)
⇒ \(y = x -3\) .....(2)
From (1) & (2),
\((x-3)^2 = 2x - 3\)
⇒ \(x^2 - 8x+ 12 = 0\)
⇒ \((x - 2) (x - 6) =0\)
⇒ \(x = 2 \;or \;x = 6\)
⇒ \(y = -1 \;or\; y = 3\)
\(\therefore P (2, - 1) \text{ & }Q(6, 3)\)
\(M_{PQ} = \frac {3 -(-1)}{6-2} = \frac 44 = 1\)
\(M_{PR} = \frac{1-(-1)}{0-2} = -1\)
\(M_{QR} =\frac{1-3}{0-6} = \frac{-2}{-6} = \frac 13\)
\(\because M_{PQ}M_{PR} = 1 \times -1 = -1\)
\(\therefore \triangle PQR\) is right angle at P.
\(\therefore\) orthocentre is P(2, -1).