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helpless06 · Nov 12, 2007, 10:39 AM

FInd the maximum and minimum value of the expression:
(y^2)/121 + (w^2)/81
if x, y, z, satisfy the following system:

x^2 + y^2 - 8x + 6y - 96 = 0
z^2 + w^2 + 10z - 4w - 52 = 0
xw + yz - 2x - 4w + 5y + 3z - 76 > 0

galactus · Nov 12, 2007, 07:48 PM

Take a look at the equations.

Here's the first.

$x^{2}-8x+y^{2}+6y=96$

Group and complete the square and it becomes:

$(x-4)^{2}+(y+3)^{2}=121$

A circle centered at (4,-3) with radius 11.