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    x = 1 - sinθ

    y = 1 + cosθ

    Need to rewrite this pair as one equation in terms of x and y, I tried all possible identities but couldn't do it, what would you do for this?
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    I'm not sure I understand the question. What comes to my mind is a parametric curve.

    \begin{cases} x=1-\sin { \theta  }  \\ y=1+\cos { \theta  }  \end{cases}

    That would result in a circle of equation (x-1)^2+(y-1)^2=1
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    The question before that one was as follows:

    x = 4secθ

    y = 2tanθ

    And the answer was x^2= 16 + 4y^2

    It's asking to combine both equations together so it's written in terms of x and y only.
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    And just looking at your post now, I see it simply forms sin^2 + cos^2 which equals 1 and it's in terms of x and y, thank you very much
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    (Original post by Rexx18)
    The question before that one was as follows:

    x = 4secθ

    y = 2tanθ

    And the answer was x^2= 16 + 4y^2

    It's asking to combine both equations together so it's written in terms of x and y only.
    So it really is about parametric curves.

    Recall that 1+\tan^2 x =\sec^2 x

    If you square your equations for x and y, you get x^2=16\sec^2 \theta and y^2=4\tan^2 \theta

    Isolating \sec^2 \theta and \tan^2 \theta, and plugging them back in the trig identity, you should get the formula for the hyperbola.
 
 
 
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