Family of Curves

Family of Plane Curves

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

Families of Curves: family of circles with center on the line y= -x and passing through the origin

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

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Find the differential equations of the following family of curves.

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.

 
 
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