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Math Help - Rectangular and parametric forms of conic sections?

  1. #1
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    Rectangular and parametric forms of conic sections?

    Find the rectangular equation of the curve whose parametric equations are given.

    1.x=-cost t, y= sin t

    2. x=-sin 2t
    y=2 cos 2t

    Now I am kind of confused what to for with the the "2t"

    For example on number 2 I did

    2 cos 2t=y
    cos2t=y/2 Would I do know square it but while I would get y^2/4 on one side what would I do on the "other side"?
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  2. #2
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    Quote Originally Posted by homeylova223 View Post
    Find the rectangular equation of the curve whose parametric equations are given.

    1.x=-cost t, y= sin t

    2. x=-sin 2t
    y=2 cos 2t

    Now I am kind of confused what to for with the the "2t"

    For example on number 2 I did

    2 cos 2t=y
    cos2t=y/2 Would I do know square it but while I would get y^2/4 on one side what would I do on the "other side"?
    You have a good start but you need to keep going and use the Pythagorean identity.

    \sin^2(x)+\cos^2(x)=1

    (-x)^2+\left( \frac{y}{2}\right)^2=1 \iff  x^2+ \frac{y^2}{4}=1
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  3. #3
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    So would the answer to my first question be

    (-x)^2+ (y)^2=1
    x^2+y^2=1
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  4. #4
    Behold, the power of SARDINES!
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    Yes
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