TYPES OF LIMACON CURVES

Looped

Equation of polar curve :

r  =  a ± b cos θ

Here a/b < 1

• If we have positive in the middle, the loop will be on right side.
• If we have positive in the middle, the loop will be on left side.

Equation of polar curve :

r  =  a ± b sin θ

Here a/b < 1

• If we have positive in the middle, the loop will be above.
• If we have positive in the middle, the loop will be below.

Cardioid

Equation of polar curve :

r  =  a ± b cos θ

Here a/b = 1

• If we have positive in the middle, the loop will be on right side.
• If we have positive in the middle, the loop will be on left side.

r  =  a ± b sin θ

Here a/b = 1

• If we have positive in the middle, the loop will be above.
• If we have positive in the middle, the loop will be below.

Dimpled

Equation of polar curve :

r  =  a ± b cos θ

Here 1 < a/b < 2

• If we have positive in the middle, the loop will be on right side.
• If we have positive in the middle, the loop will be on left side.

r  =  a ± b sin θ

Here 1 < a/b < 2

• If we have positive in the middle, the loop will be above.
• If we have positive in the middle, the loop will be below.

Equation of polar curve :

r  =  a ± b cos θ

Here a/b ≥ 2

• If we have positive in the middle, the loop will be on right side.
• If we have positive in the middle, the loop will be on left side.

r  =  a ± b sin θ

Here a/b ≥ 2

• If we have positive in the middle, the loop will be above.
• If we have positive in the middle, the loop will be below.

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