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.

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  1. 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]

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