wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The line L has intercepts a and b on the co-ordinate axes keeping the origin fixed, the co-ordinate axes are related through a fixed angle. If the same line has intercepts c and d then

A
1a2+1c2=1b2+d2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1a2+1b2=1c2+1d2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
a2+c2=b2+d2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
a2+b2=c2+d2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 1a2+1b2=1c2+1d2
Suppose we state he coordinate axis in the anti-clockwise direction through an angle α.
The equation of the line α with respect to old axes is xa+yb=1
In this equation replacing x by xcosαysinα
The equation of the line with respect to new axes is
xcosαysinαa+xsinα+ycosαb=1
x(cosαa+sinαb)+y(cosαbsinαa)=1 ...(1)
The intercept mode by (1) on the co-ordinate axes are given as c and d.
Therefore, 1c=cosαa+sinαb and 1d=cosαbsinαa
Squaring and adding, we get 1c2+1d2=1a2+1b2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Graphical Interpretation of Differentiability
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon