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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- Jan 2nd 2008, 10:59 AM #1

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- Jan 2nd 2008, 09:59 PM #2

- Jan 2nd 2008, 10:06 PM #3
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

- Jan 5th 2008, 05:53 PM #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.

- Jan 5th 2008, 06:21 PM #5
Good to see that you've had a crack at this problem.

I think there's a nice way to solve it - in fact, your working gave me the idea ......

Originally Posted by**rlarach**

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.