Question 1170535
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With the vertex at (4,1) and the directrix the line x=2, the parabola opens to the right.  The vertex form of the equation is then<br>
{{{x = ((1/(4p))(y-k)^2)+h}}}<br>
where the vertex is (h,k) and p is the directed distance from the directrix to the vertex.<br>
We are given (h,k) = (4,1); and p is the distance from the line x=2 to the point (4,1), which is 4-2=2.  So p=2 and 4p=8.  That gives us all the parts we need to write the equation:<br>
{{{x = ((1/8)(y-1)^1)+4}}}<br>