The equation of the parabola whose vertex is $(2, 0)$ and extremities of latus rectum are $(3, 2)$ and $(3, - 2)$ is 

$A(2, 0), S$ is mid-point of $L{L}^{\mathrm{\prime }}\therefore S(3,0)$

$\therefore AS=1=a.$

The axis is along x-axis and both vertex and focus are on x-axis. Hence its equation is $(y-0{)}^2=4.1(x-2)\text{ ⇒ }{y}^2=4x-8.$