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Math Help - rectangular to polar equation

  1. #1
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    rectangular to polar equation

    convert the rectangular to a polar equation:

    -8x-3y+5=0

    i know that x= r cos theta, as well as other identities

    convert the polar to a rectangular equation:
    r= 2/ (4-5 cos theta)

    i don't even know where to begin here!

    thanks
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  2. #2
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    Quote Originally Posted by ss103 View Post
    convert the rectangular to a polar equation:

    -8x-3y+5=0

    i know that x= r cos theta, as well as other identities

    Mr F says: Then substitute them into the equation and solve for r.

    convert the polar to a rectangular equation:
    r= 2/ (4-5 cos theta)

    i don't even know where to begin here!

    thanks
    r (4 - 5 \cos \theta) = 2 \Rightarrow 4r - 5 r \cos \theta = 2 \Rightarrow 4r - 5x = 2 \Rightarrow 4r = 5x + 2.

    Now square both sides and substitute x^2 + y^2 = r^2. Re-arrange into a standard form (looks like it might be a hyperbola).
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  3. #3
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    thanks!

    but for the first one, i tried to solve it but i dont know how:

    -8r cos theta - 3r sin theta +5 =0
    where do i go now? do i square it?
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  4. #4
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    Quote Originally Posted by ss103 View Post
    thanks!

    but for the first one, i tried to solve it but i dont know how:

    -8r cos theta - 3r sin theta +5 =0
    where do i go now? do i square it?
    => 8r cos theta + 3r sin theta = 5

    => r (8 cos theta + 3 sin theta) = 5

    etc.
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