What are the different types of Limacons?

There are four different-shaped limaçons: one contains an inner loop, one is the cardioid, one is dimpled, and one is convex and looks almost circular.

What shape does the polar equation form when graphed?

rose curve
Since the equation passes the test for symmetry to the polar axis, we only need to evaluate the equation over the interval [0, π] and then reflect the graph about the polar axis. The polar equation is in the form of a rose curve, r = a cos nθ.

What are graphs of polar equations?

The graph of an equation in polar coordinates is the set of points which satisfy the equation. That is, a point P(r,θ) is on the graph of an equation if and only if there is a representation of P, say (r′,θ′), such that r′ and θ′ satisfy the equation.

What are the poles of a polar graph?

The line segment starting from the center of the graph going to the right (called the positive x-axis in the Cartesian system) is the polar axis. The center point is the pole, or origin, of the coordinate system, and corresponds to r=0.

What is a limaçon curve?

Definition of limaçon : a plane curve whose equation in polar coordinates has one of the forms ρ = a cos θ ± b or ρ = a sin θ ± b and which reduces to a cardioid when a = b.

What is the difference between a limaçon and cardioid?

When the value of a is greater than the value of b, the graph is a dimpled limacon. When the value of a is greater than or equal to the value of 2b, the graph is a convex limacon. When the value of a equals the value of b, the graph is a special case of the limacon. It is called a cardioid.

How do you classify a curved polar equation?

Types of polar graphs

1. Lines: If the polar equation has a general form of r = a sin ⁡ or r = a cos ⁡ , where a ≠ 0 , its curve will be a horizontal line or a vertical line, respectively.
2. Circles: If the polar equation has a general form of r = a cos ⁡ or r = a sin ⁡ , where , its curve will be a circle with a radius of .