Question 768363
General point (x,y).
Find distance from (-5,y) to (x,y).  Find distance from (5,0) to (x,y).
EQUATE them.  You would use distance formula for both of those distance expressions.


Obtain {{{(x+5)^2=(x-5)^2+y^2}}}
.
{{{10x=-10x+y^2}}}
{{{20x=y^2}}}
{{{highlight(x=(1/20)y^2)}}}


I had drawn a representative sketch first and find vertex at left, parabola opening to the right.  Directrix is to the left of the vertex and focus is to the right of the vertex.