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

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.

## This Post Has 2 Comments

1. jholland03 says:

The type of limacon graphed is a convex.

2. DragonLovely says:

The graph is a convex limacon.

Step-by-step explanation:

Polar equation is defined as

$r=b+a\sin \theta$ and $r=b+a\cos \theta$

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

$r=4+2\sin \theta$

Here b=4 and a=2.

$2a=2(2)=4=b$

$2a=4$

$2a=b$            $[\because b=4]$

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

$What type of limacon is graphed by the polar equation r=4+2sinttheta?$