Downward Parabola
I wanted to find the simple equation of parabola having vertex at origin of coordinate axes And facing downwards$~(-y)~$
So, focus would be $~(-a,0)~$
equation of diretix would be $~(y=a)~$
As e=1 for a parabola parabola As i proceeded
Please help me where I went wrong????
Downward facing parabola would have focus as $(0,-a)$ and directrix as $y=a$. $$SP^2=PM^2$$ $${\sqrt {(x-0)^2+(y+a)^2}}=|y-a|$$ $${(x-0)^2+(y+a)^2}=(y-a)^2$$ $$x^2+y^2+a^2+2ay=y^2+a^2-2ay$$ $$x^2=-4ay$$