A parabola passes thorough the points (1,0) & (0,1) and x & y axes are tangent at these points respectively. How to find the parametric equations to such a parabola?

I have derived the equation to the parabola, which is of the "general equation of a parabola" type $\displaystyle Ax^2+Bxy+Cy^2+Dx+Ey+F=0$, not $\displaystyle y^2=4ax$ type.

The general parametric equations of a parabola are

$\displaystyle x=at^2+bt+c$

$\displaystyle y=lt^2+mt+n$

How to go about it?