Finding the Parameter of the Parabola

If we take the parabola Y=aX2 and look at the length of the horizontal chord through the focus, we find this is 1/a. Salmon calls this the parameter of the parabola. As any parabola can be rotated and translated so that its vertex is at the origin and its axis along the Y-axis, finding the canonical form is as easy as measuring the length of the length of the chord through the focus perpendicular to the axis. Expressions |
||