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Differential Equations for Curve Families

The document provides 10 problems in Section A and 10 problems in Section B asking to find the differential equation that describes various families of curves. The curves include circles, lines, parabolas, ellipses, cardioids, and roses, with specifications like fixed radii, centers on axes, tangency to other lines, and distances between vertices and foci. The problems cover basic geometric curves and their relationships to coordinate axes and each other.

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Elaine Yosores
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574 views1 page

Differential Equations for Curve Families

The document provides 10 problems in Section A and 10 problems in Section B asking to find the differential equation that describes various families of curves. The curves include circles, lines, parabolas, ellipses, cardioids, and roses, with specifications like fixed radii, centers on axes, tangency to other lines, and distances between vertices and foci. The problems cover basic geometric curves and their relationships to coordinate axes and each other.

Uploaded by

Elaine Yosores
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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PROBLEM SET 2

FIND THE DIFFERENTIAL EQUATION S OF THE FOLLOWING FAMILY OF CURVES.

Section A

1. Circles with center at the origin.

2. Circles tangent to the x axis.

3. Circles with fixed radius r and tangent to the x axis.

4. All straight lines at a unit distance from the origin.

5. Circles with center on x axis.

6. Straight lines at a fixed distance p from the origin.

7. All circles with centers on the line x y = 0 and tangent to the y axis.

8. Family of circles of variable radii r with centers on the x axis.

9. All circles in the plane.

10. Family of limacons.

Section B

1. Circles tangent to the y axis.

2. Circles with fixed radius r and tangent to the y axis.

3. Parabolas with axis parallel to the y axis with distance vertex to focus fixed as a.

4. Parabolas with axis parallel to the x axis with distance vertex to focus fixed as a.

5. Parabolas with vertex and focus on the x axis.

6. Circles with center on x axis.

7. All ellipses with center at the origin and axes on the coordinate axes.

8. Parabolas with vertex and focus on the y axis.

9. Family of cardioids.

10. Family of 3 leaf roses.

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