Recall that a parabola is a curve where any point is at an equal distance from the focus and the directrix, if (x,y) is a point on the parabola then:
[tex]\sqrt[]{(-5-x)^2+(y-0)^2}=2-y\text{.}[/tex]
Solving for y we get:
[tex]\begin{gathered} (-5-x)^2+y^2=(2-y)^2, \\ (x+5)^2+y^2=4-4y+y^2, \\ -4y=(x+5)^2-4, \\ y=-\frac{1}{4}(x+5)^2+\frac{4}{4}, \\ y=-\frac{1}{4}(x+5)^2+1. \end{gathered}[/tex]
Answer: Second option.
