Parabola with axis parallel to coordinate axis

Determine all terms (vertex; minor axis; major axis; focii; latus rectum centre; ordinate; double ordinate for ellipse with axis parallel to coordinate axis?

Ellipse with axis not parallel to coordinate axis

The differential equation of all parabolas with axis parallel to the axis of y is :

Find the equation of the parabola which has axis parallel to the y-axis and which passes through the points (0,2),(-1,0), and (1,6)

The equation of the parabola whose axis is parallel to the y -axis of the form is

Find the differential equation of all parabolas whose axis are parallel to the x-axis.

The differential equation of all parabolas whose axis are parallel to the y-axis is

Prove that the equation y^2+2ax+2by+c=0 represent a parabola whose axis is parallel to the axis of x. Find its vertex.