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29 August, 13:20

Which equation in rectangular form describes the parametric equations x=5-3cost and y=4+2sint?

A. (x+5) ^2/9 + (y+4) ^2/4=1

B. (y+4) ^2/2 - (x+5) ^2/3=1

C. (y-4) ^2/2 - (x-5) ^2/3=1

D. (x-5) ^2/9 + (y-4) ^2/4=1

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  1. 29 August, 13:23
    0
    D. (-x+5) ^2/9 + (y-4) ^2/4=1 (I assume there was a mistype)

    Step-by-step explanation:

    The first step is isolating the sine and cosine functions.

    x=5-3cos (t)

    x + 3cos (t) = 5

    3cos (t) = 5 - x

    cos (t) = (5 - x) / 3

    y=4+2sin (t)

    y - 4 = 2sin (t)

    (y - 4) / 2 = sin (t)

    Then, square at both sides of the equal sign

    cos² (t) = (5 - x) ²/3² = (5 - x) ²/9

    sin² (t) = (y - 4) ²/2² = (y - 4) ²/4

    Recall the trigonometric identity and replace.

    cos² (t) + sin² (t) = 1

    (5 - x) ²/9 + (y - 4) ²/4 = 1
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