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Middle Terms

Determine the...

Question

Determine the nature of line represented by $x^{2} + 2 x y - y^{2} = 0$ .

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Solution

$\begin{matrix} x^{2} + 2 x y - y^{2} = 0 a x^{2} + 2 h x y + b y^{2} = 0 a = 1, h = 1, b = - 1 h^{2} - a b {(1)}^{2} - 1 (- 1) 1 + 1 = 2 h = - a b > 0 r e a l a n d d i s t i c t \end{matrix}$

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