TYPES OF LIMACON CURVES
Limacon Curve :
The limacon curve are graphs of polar equations of the form
r = a ± b cos θ
(or)
r = a ± b sin θ
Where a > 0 and b > 0. Limacon can be pronounced as LEE-ma-shon is old French for "snail". There are four different shapes of limacons illustrated below.
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.
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com