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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`)

A

(a) equilateral

B

(b) Isoceles

C

(c) scalene

D

(d) none of these

Text Solution

Verified by Experts

The correct Answer is:
D
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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