1.

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)

Answer»

equilateral
right angled
scalene
none of these

Solution :The given lines are
`(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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