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

# The equation of the pair of straight lines through origin, each of which makes as angle α with the line y = x, is

A

x2+2xysec2α+y2=0

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

x2+2xycosec2α+y2=0

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

x22xycosec2α+y2=0

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

x22xysec2α+y2=0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D x2−2xysec2α+y2=0 Any line through the origin is y = mx.If it makes an angle α with the line y = x, then we should have tanα=±{m1−m21+m1m2}=±(m−1)1+m or(1+m)2tan2α=(m−1)2 ⇒m2−2m{1+tan2α1−tan2α}+1=0 ⇒m2−2msec2α+1=0, ∵{1+tan2α1−tan2α=sec2α} But m=yx, hence on eliminating m, we get the required equation y2−2xysec2α+x2=0

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Tango With Straight Lines !!
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program