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Fin the minimum and maximum of the given function

Source: Balkan MO ShortList 2007 A1

April 6, 2020
Tuzo nonsense

Problem Statement

Find the minimum and maximum value of the function \begin{align*} f(x,y)=ax^2+cy^2 \end{align*} Under the condition ax2−bxy+cy2=dax^2-bxy+cy^2=d, where a,b,c,da,b,c,d are positive real numbers such that b2−4ac<0b^2 -4ac <0
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