linguistic:voice_change
4-points property

Any parabola can be described in a suitable coordinate system by an equation y = a x 2 {\displaystyle y=ax^{2}}.

Proof: straightforward calculation for the unit parabola y = x 2 {\displaystyle y=x^{2}}.

Application: The 4-points property of a parabola can be used for the construction of point P 4 {\displaystyle P_{4}}, while P 1, P 2, P 3 {\displaystyle P_{1},P_{2},P_{3}} and Q 2 {\displaystyle Q_{2}} are given.

Remark: the 4-points property of a parabola is an affine version of the 5-point degeneration of Pascal's theorem.