Question 867542
I suggest using Distance Formula for this one and your other request post.


Use the definition for a parabola.


Unknown set of points, (x,y).
For question (a) of this posting,
The set of directrix points, a line, is (-5,y).
{{{sqrt((x-5)^2+(y-0)^2)=sqrt((x-(-5))^2+(y-y)^2)}}}
{{{sqrt((x-5)^2+y^2)=sqrt((x+5)^2+0^2)}}}
{{{sqrt((x-5)^2+y^2)=sqrt((x+5)^2)}}}
Square both sides.
{{{(x-5)^2+y^2=(x+5)^2}}}
You might not know by looking at it, but here, the x^2 terms will disappear.
{{{x^2-10x+25+y^2=x^2+10x+25}}}
{{{-10x+25+y^2=10x+25}}}
{{{-20x+25+y^2=25}}}
{{{-20x+y^2=25}}}
{{{-20x=-y^2+25}}}
{{{20x=y^2-25}}}
{{{x=(1/20)y^2-25/20}}}
{{{highlight(x=(1/20)y^2-5/4)}}}