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The product of the perpendiculars form (-1,2) to the pair of lines $2 x^{2} - 5 x y + 2 y^{2} = 0$ is

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Detailed Solution

$P = (- 1, 2)$

$G i v e n P S L 2 x^{2} - 5 x y + 2 y^{2} = 0$

$d_{1} d_{2} = | \frac{a α^{2} + 2 h α β + b β^{2}}{\sqrt{{(a - b)}^{2} + {(2 h)}^{2}}} | = | \frac{2 (1) + (- 5) (- 1) (2) + 2 (4)}{\sqrt{0 + 25}} |$

$= \frac{2 + 10 + 8}{5} = 4$

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