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If $x^{2} - y^{2} = 0, lx + 2 y = 1$ form a isosceles triangle, then $l =$

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Correct option is A

The given lines are x+y=0 …… (1) x−y=0 …… (2)And lx+2y=1 …… (3)Equations (1) and (2) represents two perpendicular lines, and the third line makes an angle with the line (1) and line (2) Hence, tan45°=m1−m21+m1m2=−l2−11−l2=l+22−l It implies that l=0

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