The vertex of the parabola y² + 6x $$-$$ 2y + 13 = 0 is

The coordinates of a moving point P are (2t² + 4, 4t + 6). Then its locus will be a/an

The locus of the middle points of all chords of the parabola y² = 4ax passing through the vertex is

The line $y-\sqrt{3} x+3=0$ cuts the parabola $y^2=x+2$ at the points $P$ and $Q$. If the co-ordinates of the point $X$ are $(\sqrt{3}, 0)$, then the value of $X P \cdot X Q$ is