The equation for a parabola does become [tex]\rm x^2=4py[/tex].
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;
[tex]\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[/tex]
Hence, the equation for a parabola does become [tex]\rm x^2=4py[/tex].
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