I want to confirm this, i want to draw an arch, knowing its shape, which is the parabolic equation ax^2+bx+c, knowing its end and final point and its lenght, not the coord, the real length of the arch (all these pararmeters it is me that decide them), what i think is if you know the starting and end points and you the length, knowing that is can only assume a specific shape you only have two solutions, one is the mirror of the other, however i cant define or the radius or the arch equation, i am hoping someone can enlighten me about this.

thank you