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Math Help - Please help!

  1. #1
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    Smile Please help!

    Assume that x and y are real numbers such that :

    (x + 5)^2 + (y - 12)^2 = 196

    What is the maximum value of the quantity x^2 + y^2 ?


    Thank you very much for your help!! I appreciate it!
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  2. #2
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    Quote Originally Posted by rlarach View Post
    Assume that x and y are real numbers such that :

    (x + 5)^2 + (y - 12)^2 = 196

    What is the maximum value of the quantity x^2 + y^2 ?


    Thank you very much for your help!! I appreciate it!
    Not that I've bothered working the details (becuase for one thing I don't know your mathematical background), but the method of Lagrange multipliers comes to mind as a simple general approach to try .....

    But no doubt there's another - tricky fancy - way.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mr fantastic View Post
    Not that I've bothered working the details (becuase for one thing I don't know your mathematical background), but the method of Lagrange multipliers comes to mind as a simple general approach to try .....

    But no doubt there's another - tricky fancy - way.
    you know i have no experience with Lagrange multipliers

    i was thinking of doing something along the lines of expanding the left hand side and solving for x^2 + y^2. so you would have x^2 + y^2 = f(x,y), where f(x,y) is, of course, a function of x and y. then you would proceed to minimize that function. but that seems like calc 3 stuff. and maybe is too much work anyway
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  4. #4
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    What I tried doing was to get the center of this circle (assuming it is one) to be (-5,12) an the radius 14. Then I took each extrem (up down left and right ) and I did 26 squared plus 25 to get 701. But I'm not sure if there are other coordinates on the circle with a greater value when the squares are summed.
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  5. #5
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    Quote Originally Posted by rlarach View Post
    What I tried doing was to get the center of this circle (assuming it is one) to be (-5,12) an the radius 14. Then I took each extrem (up down left and right ) and I did 26 squared plus 25 to get 701. But I'm not sure if there are other coordinates on the circle with a greater value when the squares are summed.
    Good to see that you've had a crack at this problem.

    Quote Originally Posted by mr fantastic View Post
    Not that I've bothered working the details (becuase for one thing I don't know your mathematical background), but the method of Lagrange multipliers comes to mind as a simple general approach to try .....

    But no doubt there's another - tricky fancy - way.
    I think there's a nice way to solve it - in fact, your working gave me the idea ......

    Quote Originally Posted by rlarach
    What I tried doing was to get the center of this circle (assuming it is one) to be (-5,12) an the radius 14.
    This is correct. What you now want is the circle C of the form x^2 + y^2 = r^2 that intersects the circle (x + 5)^2 + (y - 12)^2 = 196 and has the largest possible value of r.

    If you think about it, you'll see that by symmetry the intersection of the line passing through (0, 0) and (-5, 12) with the circle (x + 5)^2 + (y - 12)^2 = 196 will give you the coordinates of a point on C. Use that point to get the value of r^2 and hence x^2 + y^2.

    I think that should work. The details are left for you.
    Last edited by mr fantastic; January 5th 2008 at 09:17 PM. Reason: Added a quote and re-ordered quotes
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