Question 1191710
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You don't need to use the "equal distance" information to write and simplify an equation that says the distance from the point is equal to the distance from the line.<br>
The given information defines a parabola with directrix x=-2 and focus (2,3).<br>
With directrix x=-2 and focus (2,3), the vertex is (0,3).  The parabola opens to the right; the equation in vertex form is <br>
{{{x-h=(1/(4p))(y-k)^2)}}}<br>
where (h,k) is the vertex and p is the directed distance (i.e., could be negative) from the vertex to the focus.<br>
In this problem, (h,k) is (0,3) and p is 2.  So the equation is<br>
{{{x-0=(1/8)(y-3)^2}}}<br>
or<br>
{{{x=(1/8)(y-3)^2}}}<br>
or<br>
{{{8x=(y-3)^2}}}<br>