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If p is the length of the perpendicular ...

If p is the length of the perpendicular from the origin to the line, whose intercepts with the coordinate axes are `1/3` and `1/4`, then the value of p is :

A

`(3)/(4)`

B

`(1)/(12)`

C

`5`

D

`(1)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
D
Equation of line in intercept form is `(x)/(a)+(y)/(b)=1`
Here, `a=1//3 and b=1//4`
`therefore(x)/(1//3)+(y)/(1//4)=1`
`implies3x+4y=0`
Now, perpendicular distance from
(0,0) to the ilne is
`(|3(0)+4(0)-1|)/(sqrt(3^(2)+4^(2)))=p`
`implies(1)/(sqrt(9+16))=p`
`p=(1)/(5)`
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