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The foot of the perpendicular on the lin...

The foot of the perpendicular on the line `3x+y=lambda` drawn from the origin is `Cdot` If the line cuts the `x` and the y-axis at `Aa n dB` , respectively, then `B C: C A` is
(a)`1:3`
(b) `3:1`
(c) `1:9`
(d) `9:1`

A

`1:3`

B

`3:1`

C

`1:9`

D

`9:1`

Text Solution

Verified by Experts

The correct Answer is:
D
`tan180^@-theta)=`Slope of `AB=-3`
`thereforetan theta=3`
`therefore(OC)/(AC)=tantheta,(OC)/(BC)=cottheta`
or `(BC)/(AC)=(tantheta)/(cottheta)=tan^2theta=9`
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