The foot of the perpendicular drawn from the origin, on the line, 3x+y=λ(λ≠0) is P. If the line meets x-axis at A and y-axis at B, then the ratio BP:PA is :
A
1:9
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1:3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3:1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
9:1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is D9:1 Let the equation of line is 3x+y=λ...(1)
slope of AB=−3 ∴ slope of OP=13
Equation of OP is y−0=13(x−0) ⇒x=3y
Put in equation (1) ⇒9y+y=λ ⇒y=λ10
Suppose P divides AB into m:n ∴3λ10=m⋅0+n⋅λ3m+n ⇒mn=19
Hence, BP:AP=n:m=9:1