A parabola has its vertex at the origin. Its focus lies on the $y$y-axis, $4$4 units above the vertex.
State the equation of the parabola.
A parabola has its vertex at the origin. It has a focal length measuring $a=4$a=4 units, and its focus lies on the $x$x-axis.
State both possible equations of the parabola.
Find the equation of the parabola with a focus at $\left(0,3\right)$(0,3) and a vertex at the origin. Let $a$a represent the focal length if necessary.
Find the equation of the parabola with a focus at $\left(-6,0\right)$(−6,0) and a vertex at the origin. Let $a$a represent the focal length if necessary.