Question 1012198
{{{4py=x^2}}} can be a parabola with vertex at the origin, and opening upward.  Using different symbols, the parabola can also be {{{y=ax^2}}} and has points (-6,8) and (6,8).


Find the factor, a.
{{{8=a*6^2}}}, using the simpler formula.
{{{a=8/36}}}
{{{a=2/9}}}
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The equation for the parabola more specifically can be  {{{highlight(y=(2/9)x^2)}}}.


What about the focus?
Put the equation with the p into the same form as the more specific-found equation.  The value of p is THE DISTANCE FROM VERTEX TO FOCUS.
{{{4py=x^2}}}
{{{y=(1/(4p))x^2}}}
Comparing the corresponding equation parts, 
{{{2/9=1/(4p)}}}
{{{9/2=4p}}}
{{{p=9/(2*4)}}}
{{{highlight(p=9/8)}}}.


The focus will be on the "opening upward" side of the parabola, as described in this discussion, above the origin, so the focus is  {{{highlight(9/8=1&1/8)}}} inches away from the vertex.  Inside of the curve.