Question 1119191
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The vertex form of the equation of a parabola that opens to the right with vertex (h,k) is<br>
{{{(x-h) = (1/(4p))(y-k)^2}}}<br>
In that formula, p is the directed distance from the vertex to the focus; since in this problem the parabola opens to the right, p is positive.<br>
Then, since the vertex is (0,0) and the directed distance p from the vertex to the focus is 7, the equation is<br>
{{{(x-0)^2 = (1/4(7))(y-0)^2}}}<br>
or<br>
{{{x = (1/28)(y^2)}}}