My question is: Write the equation of the parabola with focus (1,1), whose normal focal chord is parallel to the x-axis and has length 8. Find its apex, the equation of its directrix and the equation of its axis.
I solved this question and I got two equations of parabolas satisfying the given conditions: \begin{align*} (x-1)^2 = 8 (y+1) \end{align*} and \begin{align*} (x-1)^2 = -8(y-3). \end{align*} Is that true? I want only to make sure that the parabola is not unique.
Thanks in advance.