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Math Help - find the difference between the centers of circles

  1. #1
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    Unhappy find the difference between the centers of circles

    Can someone tell me if this is right?
    The equation of Circle P is x2 + y2 − 6x + 4y = 21 and the equation of circle Q is x2 + y2 − 8x + 10y = 11. What is the distance between the centers of these circles?

    Circle p
    (x-6)2+(y+4)2=21
    x2+36+y2+16=21
    x2+y2=21-36-16=-31
    x2+y2=-31squared
    Circle Q
    x2+y2-8x+10y=11
    (x-8)2+(y+10)2=11
    x2+64+42+100=11
    x2+y2=11-164=-153

    answer -153-31=122 is the difference?
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  2. #2
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    Quote Originally Posted by sanee66 View Post
    Can someone tell me if this is right?
    The equation of Circle P is x2 + y2 − 6x + 4y = 21 and the equation of circle Q is x2 + y2 − 8x + 10y = 11. What is the distance between the centers of these circles?

    Circle p
    (x-6)2+(y+4)2=21
    x2+36+y2+16=21
    x2+y2=21-36-16=-31
    x2+y2=-31squared
    Circle Q
    x2+y2-8x+10y=11
    (x-8)2+(y+10)2=11
    x2+64+42+100=11
    x2+y2=11-164=-153

    answer -153-31=122 is the difference?
    No, if you had done everything else right that would be the difference in the radii of the two circles.

    Circle P has equation: x^2+y^2-6x+4y=21.

    Which after completing the square for x and y on the left hand side, can be rewritten as:

    <br />
(x-3)^2 + (y+2)^2=21-9-4= 8<br />

    So the centre of circle P is at (3,-2).

    Now do the same for circle Q, and then find the distance between the centres of the circles.

    RonL
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  3. #3
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    Lightbulb Did I get difference between the centers of circles

    So is this right?
    Circle P
    x2+y2-6x+4y=21
    x2-6x+y2+4y=21
    x-3)2+(y+2)2=21
    x2+9+y2+4=21
    x2+y2-9-4=21-9-4=8
    Center is at (3,-2
    Circle Q
    x2+y2-8x+10y=11
    x2-8x+y2+10y=11
    x-4)2+(y+5)2=11
    x2+16+y2+25=11
    x2+y2-16-25=11+16+25=52
    Center is at (4,-5)
    Distance between is (1,-3)
    Last edited by sanee66; July 18th 2007 at 01:46 PM. Reason: Getting rid of characters
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  4. #4
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    Quote Originally Posted by CaptainBlack View Post
    <br />
(x-3)^2 + (y+2)^2=21-9-4= 8<br />
    Quote Originally Posted by sanee66 View Post
    x-3)2+(y+2)2=21
    You didn't factor correctly

    (y+2)^2=(y+2)(y+2)=y^2+4y+4\neq y^2+4

    same thing with x-3
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