Family of Curves

Find the differential equation of parabolas with vertex and focus on the x-axis.

Find the diff equation of family of circles with center on the line y= -x and passing through the origin.

THANK YOU :)

Differential Equations
Find the differential equations of the following family of curves.

1. Parabolas with axis parallel to the y – axis with distance vertex to focus fixed as a.
2. Parabolas with axis parallel to the x – axis with distance vertex to focus fixed as a.
3. All ellipses with center at the origin and axes on the coordinate axes.
4. Family of cardioids.
5. Family of 3 – leaf roses.