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circle geometry - translation - C1 Watch

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    question: write down the equation of the circle which is obtained by applying the given translation to the given circle:

    -1
    2

    (that's supposed to be the vector idk how to do extended square brackets)

    the given circle: x2 + y2 - 4x + 2y = 4

    what I did was group the x & y's and complete the square to get (x-2)2 + (y+1)2 = 9 and then applied the translation to get an answer of: (x -1)2 + (y-3)2 = 9

    but in the answers it says: x2 + y2 - 2x - 2y = 7

    even if I expand out the answer that I got, I don't get the same - can someone please tell me what I've wrong

    and also how to directly apply a translation to an equation in same form as the one in the question without having to complete the square
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    It's the y part you have done incorrectly.
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    (Original post by batoot)
    question: write down the equation of the circle which is obtained by applying the given translation to the given circle:

    -1
    2

    (that's supposed to be the vector idk how to do extended square brackets)

    the given circle: x2 + y2 - 4x + 2y = 4

    what I did was group the x & y's and complete the square to get (x-2)2 + (y+1)2 = 9 and then applied the translation to get an answer of: (x -1)2 + (y-3)2 = 9

    but in the answers it says: x2 + y2 - 2x - 2y = 7

    even if I expand out the answer that I got, I don't get the same - can someone please tell me what I've wrong

    and also how to directly apply a translation to an equation in same form as the one in the question without having to complete the square
    You should always complete the square for equation of a circle - that is the standard form it is notmally in.
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    (Original post by Ano123)
    It's the y part you have done incorrectly.
    i don't get where though, I just checked through my working again
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    (Original post by batoot)
    i don't get where though, I just checked through my working again
    The y-coordinate of the centre is (, -1) - if you shift this up by two units, you should get it (, +1), so your new equation should be...?
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    (Original post by Zacken)
    The y-coordinate of the centre is (, -1) - if you shift this up by two units, you should get it (, +1), so your new equation should be...?
    ooooooooh -1
    so it should be
    (x -1)2 + (y-1)2 = 9

    I can't believe I didn't see that -.- I always make stupid mistakes, thank you
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    (Original post by batoot)
    ooooooooh -1
    so it should be
    (x -1)2 + (y-1)2 = 9

    I can't believe I didn't see that -.- I always make stupid mistakes, thank you
    No problemo. :-)
 
 
 
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