Position of a point on parabola

Position of a point

P(x₁, y₁) will be outside, inside or on the parabola according as

y₁₂ − 4ax₁ > 0, < 0 or = 0.

Length of the chord intercepted by the parabola y² = 4ax from the line y = mx + c is given by .

Point on a parabola

Coordinate of any point on the parabola ^y2 = 4ax in the parametric form are (at₂, 2at).