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The combined equation of the diagonals of the square formed by the pair of lines $x y + 4 x - 5 y - 20 = 0$ and $x y - 5 x + 4 y - 20 = 0$ is $x^{2} - y^{2} - k x + l y = 0$ then $k + l$

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Detailed Solution

$x y + 4 x - 5 y - 20 = 0$

$\Rightarrow (x - 5) (y + 4) = 0$

$x y - 5 x + 4 y - 20 = 0$

$\Rightarrow (x + 4) (y - 5) = 0$

$\Rightarrow A (- 4, - 4), B (5, - 4), C (5, 5), D (- 4, 5)$

$\bar{A C}$ is $x - y = 0$

$\bar{B D}$ is $x + y - 1 = 0$

$(x - y) (x + y - 1) = 0$

$x^{2} + y^{2} - x + y = 0$

$k + l = 1 + 1 = 2$

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