Suppose a parabola passes through $$(0,4),(1,9)$$ and $$(4,5)$$ and has its axis parallel to the $$Y$$-axis. Then, the equation of the parabola is

Suppose a parabola with focus at $$(0,0)$$ has $$x-y+1=0$$ as its tangent at the vertex. Then, the equation of its directrix is

If $$a x+b y=1$$ is a normal to the parabola $$y^2=4 p x$$, then the condition is

The coordinates of the focus of the parabola described parametrically by $$x=5t^2+2$$ and $$y=10t+4$$ (where t is a parameter) are