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A line passes through (2,0). Then which ...

A line passes through (2,0). Then which of the following is not the slope of the line, for which its intercept between `y=x-1` and `y=-x+1` subtends a right angle at the origin?

A

`-(1)/(sqrt(3))`

B

`-sqrt(3)`

C

`(1)/(sqrt(3))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
The joint equation of straight line `y = x -1` and `y =- x +1` is
`(x-y-1) (x+y-1) =0`
`rArr x^(2) -y^(2) -2x +1 =0` (i)
Let equation of line passes through (2,0) is
`y = m (x-2)`
By homogenizing equation (i) with help of line (ii), we get
`x^(2)-y^(2)-2x ((mx-y)/(2m)) +((mx-y)/(2m))^(2) =0`
This is pair of straight line through origin. Since these lines are perpendicular,
Coefficiennt of `x^(2) +` coefficient of `y^(2) =0`
`rArr m = +- (1)/(sqrt(3))`
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