Recall that a parabola is a curve where any point is at an equal distance from the focus and the directrix, then, if (x,y) is a point on the parabola, we can set the following equation:
[tex]\sqrt[]{(x-6)^2+(y-2)^2}=y-0=y.[/tex]
Solving for y we get:
[tex]\begin{gathered} (x-6)^2+(y-2)^2=y^2, \\ (x-6)^2+y^2-4y+4=y^2, \\ (x-6)^2+4=4y, \\ y=\frac{1}{4}(x-6)^2+1. \end{gathered}[/tex]
Answer: First option.
