The straight lines represented by the equation `135 x^2-136 x y+33 y^2=0` are equally inclined to the line `x-2y=7` (b) x+2y=7 `x-2y=4` (d) `3x+2y=4`

Question

The straight lines represented by the equation `135 x^2-136 x y+33 y^2=0` are equally inclined to the line `x-2y=7` (b) x+2y=7 `x-2y=4` (d) `3x+2y=4`

The straight lines represented by the equation `135 x^2-136 x y+33 y^2=0` are equally inclined to the line `x-2y=7` (b) x+2y=7 `x-2y=4` (d) `3x+2y=4`
A. `x-2y=7`
B. `x+2y=7`
C. `x-2y=4`
D. `3x+2y=4`

Monjur Alahi

4 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 - 2
The given pair of lines is
`135x^(2)-136xy+33y^(2)=0` (1)
the equation of bisectors of angles between the pairs of lines (1) is
`(x^(2)-y^(2))/(a-b)=(xy)/(h)or(x^(2)-y^(2))/(135-33)=(xy)/(-68)`
or `2x^(2)+3xy-2y^(2)=0`(2)
or `(x+2)(2x-y)=0`
One of the bisectors is `x+2y=0` which is parallel to the line `x+2y=7`.
Hence , the line `x+2y=7` is equally inclined to the given lines.