Crazy Gaussian Integral

Calculus Level 5

If the following integral is satisfied for some relationship between the constants \(a , b\) and \(c\)-

\[ \displaystyle\int_{-∞}^{∞}\displaystyle\int_{-∞}^{∞} e^{-(ax^{2} + 2bxy + cy^{2})}dxdy = 1\]

Find the value of \( b^{2} -ac \)

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