Answer
$${\text{parabola}}$$
Work Step by Step
$$\eqalign{
& x - 4{y^2} - 8y = 0 \cr
& 4{y^2} + 8y = x \cr
& {\text{Divide both sides by }}4 \cr
& {y^2} + 2y = \frac{1}{4}x \cr
& {\text{Complete the square and factor}} \cr
& {y^2} + 2y + 1 = \frac{1}{4}x + 1 \cr
& {\left( {y + 1} \right)^2} = \frac{1}{4}\left( {x + 4} \right) \cr
& {\text{The equation is written in the form }}{\left( {y - k} \right)^2} = 4p\left( {x - h} \right) \cr
& {\text{Therefore,}} \cr
& {\text{The graph of the equation is a parabola}} \cr} $$
