## Family of Plane Curves

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

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

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**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.