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Math Help - Coordinates Geometry of circle

  1. #1
    Member helloying's Avatar
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    Coordinates Geometry of circle

    two circles, x+y-2x-3y=0,
    x+y+x-y-6=0

    intersect at points P and Q. Find the length of PQ and eq of the line PQ.

    Tell me wat i shld do?
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by helloying View Post
    two circles, x+y-2x-3y=0,
    x+y+x-y-6=0

    intersect at points P and Q. Find the length of PQ and eq of the line PQ.

    Tell me wat i shld do?
    [1]: x^2+y^2-2x-3=0

    [2]: x^2+y^2+x-y-6=0

    Calculate [2] - [1]:

    3x+2y-6=0~\implies~y=-\dfrac32x+3 Substitute the term for y into equation [1]:

    x^2+\left(-\dfrac32x+3 \right)^2-2x-3\left(-\dfrac32x+3\right)=0~\implies ~ \dfrac{13}4x^2-\dfrac{13}2x=0\implies~x=0~\vee~x=2

    That means the coordinates of P and Q are: P(0,3), Q(2,0)

    Now use 2-point-formula of a straight line to get the equation of PQ.

    Use distance formula to calculate the length of \overline{PQ}

    EDIT: See attachment
    Attached Thumbnails Attached Thumbnails Coordinates Geometry of circle-schnit_zweikreise.png  
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