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`)

Question

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`)

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. equilateral
B. right angled
C. scalene
D. none of these

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - 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.