Question: Show that the maximum value of the function f (x, y) = (ax + by + c) 2 /x 2 + y 2 + 1

Show that the maximum value of the function

f (x, y) = (ax + by + c)2/x2 + y2 + 1

is a2 + b2 + c2.
One method for attacking this problem is to use the Cauchy-Schwarz Inequality:
|a • b | < |a||b|

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