1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

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

A

3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

13

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

12

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A 3 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 y−λa1+λ=x−a1+λ or x−y=1−λ1+λa So, the coordiantes of M are (0,λ−1λ+1a) Therefore, area of the triangle AMN is =12∣∣∣[a(−aλ+1)+1−λ(1+λ)2a2]∣∣∣=λa2(1+λ)2 Also area of the triangle OAB = a22 So that according to the given condition. λa2(1+λ)2=38.12a2⇒ 3λ2−10λ+3=0⇒ λ=3 or λ=13 For λ=13, M lies outside the segment OB and hence the required value of λ is 3.

Suggest Corrections
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program