Finding the Parameter of the Parabola

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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

Name Input
Distance of Chord Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image