FIND THE EQUATION OF LIMACONS CURVE

To know about types of limacon curves, please visit the following page

Type of Limacon Curves

Example 1 :

Write the equation of limcaon curve of the following graph.

Solution :

By analyzing the given picture, we can find the following points.

In general the given shape is a loop, so a/b < 1.

Minimum point  ==>  b - a  =  1  -------(1)

Maximum point  ==>  b + a  =  5  -------(2)

(1) + (2)

2b  =  6

b  =  3

By applying the value of b in (1), we get

3 - a  =  1

a  =  3 - 1

a  =  2

General form of limacons :

Since the graph is symmetric about x axis and on the left side, the general form will be

r  =  a - b cos θ

r  =  2 - 3 cos θ

Example 2 :

Write the equation of limcaon curve of the following graph.

Solution :

By analyzing the given picture, we can find the following points.

In general the given shape is dimpled. So, 1 < a/b < 2.

Minimum point  ==>  b - a  =  1  -------(1)

Maximum point  ==>  b + a  =  7  -------(2)

(1) + (2)

2b  =  8

b  =  4

By applying the value of b in (1), we get

4 - a  =  1

a  =  4 - 1

a  =  3

General form of limacons :

Since the graph is symmetric about x axis and on the right side, the general form will be

r  =  a + b cos θ

r  =  3 + 4 cos θ

Example 3 :

Write the equation of limacon curve of the following graph.

Solution :

By analyzing the given picture, we can find the following points.

In general the given shape is a loop, so a/b < 1.

Minimum point  ==>  b - a  =  1  -------(1)

Maximum point  ==>  b + a  =  5  -------(2)

(1) + (2)

2b  =  6

b  =  3

By applying the value of b in (1), we get

3 - a  =  1

a  =  3 - 1

a  =  2

General form of limacons :

Since the graph is symmetric about y axis and below, the general form will be

r  =  a - b sin θ

r  =  2 - 3 sin θ

Example 4 :

Write the equation of limcaon curve of the following graph.

Solution :

By analyzing the given picture, we can find the following points.

In general the given shape is a cardioid.

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