The equation of parabola whose focus is $(6,0)$ and directrix is $x=-6$ is

If the parabola $$y=\alpha x^2-6 x+\beta$$ passes through the point $$(0,2)$$ and has its tangent at $$x=\frac{3}{2}$$ parallel to $$X$$-axis, then

If the parabola $$x^2=4$$ ay passes through the point $$(2,1)$$, then the length of the latus rectum is