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If a line is perpendicular to the line 5...

If a line is perpendicular to the line `5x-y=0` and forms a triangle with coordinate axes of area `5` sq. units, then its equation is :

A

`x+5y pm 5sqrt(2)=0`

B

`x-5y pm 5sqrt(2)=0`

C

`5x+y pm 5sqrt(2)=0`

D

`5x - y pm 5sqrt(2)=0`

Text Solution

Verified by Experts

The correct Answer is:
A
`5x-y=0`
`y=5x` ...(i)
Slope `=5`
Slope of perpendicular line will be `-1/5`.
Let equation of line is
`y=(-1/5)x+c` ...(2)
Putting `y=0`
`x=5c`
`OB=5c`
Intersecting point A

Putting `x=0`
`y=-1/5xx0+c`
`y=c`
area `Delta AOB =1/2 xxcxx5c`
`5=1/2xx5c^(2)`
`c= pm sqrt(2)`
`y=(-1/5)x pm sqrt(2)`
`5y+x pm 5sqrt(2)=0`
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