In a plane, the locus (or set) of points with the same distance to a fixed point F and a fixed line L that does not pass through F is called parabola. In addition, f is called "the focus of parabola" and l is called "the directrix of parabola".

Define the distance from the focal point to the parabolic directrix as "focal length" and use p>0.

Insert the tangent plane into a cone parallel to the ground to get a circle. If you tilt the plane parallel to one side, you can make a parabola.

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2. The standard equation of parabola

Parabola has four standard equations:

Parabola with right opening: y 2 = 2px

Left open parabola: y 2 =-2px

Upper parabola: x 2 = 2py

Parabola of lower opening: x 2 =-2py

P is the focal length (p>0).

In parabola y 2 = 2px, the focus is (p/2,0), and the equation of directrix L is x =-p/2; In the parabola y 2 =-2px, the focus is (-p/2,0), and the equation of the directrix L is x = p/2; In parabola x 2 = 2py, the focus is (0, p/2), and the equation of directrix L is y =-p/2; In parabola x 2 =-2py, the focus is (0, -p/2), and the equation of directrix L is y = p/2;