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If $x^{2} + α y^{2} + 2 β y = a^{2}$ represents a pair of perpendicular lines, then $β =$

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Detailed Solution

$x^{2} + α y^{2} + 2 β y = a^{2}$ represents a pair of perpendicular lines $\Rightarrow α = - 1$ $a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 0$

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