Question

If the equation is further simplified, which equation for a parabola does it become? x2 = 4py x2 = 2y2 2p2 y2 = 4px y2 = 4py.

Answer 1

The equation for a parabola does become $\rm x^2=4py$.

What is parabola?

A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.

Given

The derivation for the equation of a parabola with a vertex at the oriin.

The equation of the parabola can be written as;

$\rm (x)^2 + (y - p)^2 = (0)2 + (y + p)2\\\\x^2 + y^2 - 2py + p^2 = y^2 + 2py + p^2\\\\ x^2= 2py+2py\\ \rm \\x^2=4py$

Hence, the equation for a parabola does become $\rm x^2=4py$.

To know more about parabola click the link given below.

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