CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The line x + y  = a meets the axes of x and y at A and B respectively. A triangle AMN is inscribed in the ΔOAB, O being  the origin, with right angle at N. M and N lie respectively on OB and AB.  If the area of the ΔAMN is 38 of the area of the ΔOAB, then ANBN is equal to



A

loader
B

loader
C

loader
D

loader

Solution

The correct option is D


Let ANBN=λ.Then,the coordinates of N are(a1+λ,λa1+λ)

Where (a, 0) and (0, a) are the coordinates of A and B respectively. Now, equation of MN perpendicular to AB is

yλa1+λ=xa1+λxy=1λ1+λaSo,the coordinates of M are(0,λ1λ+1a)=12[a(aλ+1)+1λ(1λ)2a2]Also,area of the ΔOAB=a22So,that according to the given condition.λa2(1+λ)2=38.12a23λ210λ+3=0λ=3λ=13or 13Forλ=13,M lies outside the segment OB and hence the required value of λ is 3.Hence,(d)is the correct answer.


Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image