The derivation for the equation of a parabola with a vertex at the origin is started below. = startroot (x minus 0) squared (y minus p) squared endroot = startroot (x minus x) squared (y minus (negative p)) squared endroot (x)2 (y – p)2 = (0)2 (y p)2 x2 y2 – 2py p2 = y2 2py p2 if the equation is further simplified, which equation for a parabola does it become? x2 = 4py x2 = 2y2 2p2 y2 = 4px y2 = 4py

The equation of parabola it becomes will be x²= 4py.The y-axis passes through (0, -a), and the directrix of the parabola x² = 4ay has the equation y + a = 0

What is a parabola?

A parabola is a curve in which all points are at the same distance from two fixed points: the focus and a fixed straight line (the directrix ).

The given expression in the problem is;

[tex]x^2 +y^2-2py +p^2= y^2+2py+p^2[/tex]

On simplifying the gIven expression we get;

[tex]x^2- 2py = 2py \\\\ x^2= 2py+2py \\\\x^2=4py[/tex]

The y-axis passes through (0, -a), and the directrix of the parabola x²= 4ay has the equation y + a = 0. The y-axis passes through (0, a), and the center of the parabola x2 = -4ay has the equation y - a = 0.

Hence the equation of parabola it becomes will be x²= 4py

To learn more about the parabola refer to the link;

https://brainly.com/question/8495504

CaramelsAlcremie CaramelsAlcremie · Answer 2 · 2022-04-26T19:48:06+02:00

CaramelsAlcremie CaramelsAlcremie

26-04-2022

Answer:

The answer is A: x2 = 4py

Step-by-step explanation:

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