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Triangle formed by variable lines (a+b)x+(a-b)y-2ab=0 and (a-b)x+(a+b)y-2ab=0 and x+y=0 is (where a, b in R) |
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Answer» equilateral `(a+b)X+(a-b)y-2ab=0 "" (1)` `(a-b)x+(a+b)y-2ab=0 "" (2)` `"and " x+y=0 "" (3)` Lines (1) and (2) are symmetrical about the line y=x (as on interchanging x and y in `1^(ST)` line gives `2^(ND)` line). So, y=x is one of the angle BISECTORS. This is perpendicular to the third side x+y=0. Therefore, triangle is isosceles. |
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