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Perpendicular foot drawn from the origin...

Perpendicular foot drawn from the origin to the line `3x+y-lambda` is C. If line intersects x and y axes at points A and B respectively, then BC:CA is a. 1:3 b. 3:1 c. 1:9 d. 9:1

Text Solution

Verified by Experts

`OC=|-lambda/sqrt(3^2+1^2)|=lambda/sqrt10`
`In/_OCB`
`BC=sqrt(lambda^2-(lambda/sqrt10)^2)`
`BC=sqrt(9/10*lambda^2`
`In /_OCA`
`CA=sqrt((lambda/3)^2-(lambda/sqrt10)^2)` `CA=sqrt(lambda^2/90)` `ratio=(BC)/(CA)=sqrt((9lambda^2)/10)/sqrt(lambda^2/10)`
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