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26 March, 22:43

Which conic section is represented by the polar equation r=3 / (4+2sintheta) ?

A. ellipse

B. hyperbola

C. parabola

D. circle

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Answers (1)
  1. 26 March, 23:03
    0
    The conic is an ellipse ⇒ answer A

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - The polar form equation of a conic with a focus at the origin, the

    directrix is y = ± p where p is a positive real number, and the

    eccentricity is a positive real number e is r = ep / (1 ± e sin Ф)

    # If 0 ≤ e <1, then the conic is an ellipse

    # If e = 1, then the conic is a parabola

    # If e > 1, then the conic is an hyperbola

    - Lets solve the problem

    ∵ The equation of the conic is r = 3 / (4 + 2 sin Ф)

    ∵ The form of the equation is r = ep / (1 ± e sin Ф)

    - We must divide up and down by 4 to make the 1st term of the

    denominator equal 1

    ∴ r = (3/4) / (1 + (2/4) sin Ф)

    ∴ ep = 3/4

    ∴ e = 2/4

    - Lets use the rules above to identify the type of the conic

    ∵ e = 2/4 = 1/2

    ∴ 0 ≤ e < 1

    ∴ The conic is an ellipse
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