Question 893188
The parabola is the set of points (x,y) equally distant from (0,-5) as from (x,5).


DISTANCE FORMULA will let you derive the specific parabola.


{{{sqrt((x-0)^2+(y-(-5))^2)=sqrt((x-x)^2+(y-5)^2)}}}

{{{sqrt(x^2+(y+5)^2)=sqrt(0+(y-5)^2)}}}

{{{x^2+(y+5)^2=(y-5)^2}}}

Symmetric Property of Equality:
{{{(y-5)^2=x^2+(y+5)^2}}}
{{{y^2-10y+25=x^2+y^2+10y+25}}}
{{{-10y=x^2+10y}}}
{{{-20y=x^2}}}
{{{20y=-x^2}}}
{{{highlight(y=-(1/20)x^2)}}}