Semicubical parabola/Equation for image/Exercise

Let ${}K$ be a field. The image of the curve defined by

$K\longrightarrow K^{2},t\longmapsto \left(t^{2},\,t^{3}\right),$

is called semicubical parabola. Show that a point ${}(x,y)\in K^{2}$ belongs to this image if and only if it satisfies the equation ${}x^{3}=y^{2}$.

Create a solution