What type of limacon is graphed by the polar equation r=4+2 sin Θ? Identify the axis of symmetry and horizontal and vertical intercepts.

Skip to content# What type of limacon is graphed by the polar equation r=4+2 sin Θ? Identify the axis of symmetry and horizontal and vertical

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What type of limacon is graphed by the polar equation r=4+2 sin Θ? Identify the axis of symmetry and horizontal and vertical intercepts.

The type of limacon graphed is a convex.

The graph is a convex limacon.

Step-by-step explanation:

Polar equation is defined as

[tex]r=b+a\sin \theta[/tex] and [tex]r=b+a\cos \theta[/tex]

Types of limacon:

1. If b < a, then graph is a limacon with and inner loop.

2. If a < b < 2a, then graph is a dimpled limacon.

3. If 2a ≤ b, then graph is a convex limacon.

The given equation is

[tex]r=4+2\sin \theta[/tex]

Here b=4 and a=2.

[tex]2a=2(2)=4=b[/tex]

[tex]2a=4[/tex]

[tex]2a=b[/tex] [tex][\because b=4][/tex]

Since 2a ≤ b, therefore the graph is a convex limacon.

[tex]What type of limacon is graphed by the polar equation r=4+2sinttheta?[/tex]