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!
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
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.
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.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.