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

Let (x,y) be foot of perpendicular drawn to the point (x1,y1) on the line ax+by+c=0
Relation : x−x1a=y−y1b=−(ax1+by1+cz1)a2+b2
Here (x1,y1)=(0,0)
given line is: 3x+y−λ=0
x/3=y/1=−((3×0)+(1×0)−λ)32+12
x=3λ/10 and y=λ/10
Hence foot of perpendicular P=(3λ/10,λ/10)
Line meets X-axis at A=(λ/3,0) and meets Y-axis at B=(0,λ)
BP=√(3λ/10)2+(λ/10−λ)2 ⇒BP=√9λ2/100+81λ2/100 ∴BP=√90λ2/100
AP=√(λ/3−3λ/10)2+(0−λ/10)2 ⇒AP=√λ2/900+λ2/100 ∴AP=√10λ2/900
∴BP:AP=9:1
Hence, correct option is 'A'.