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

A variable line drawn through the point of intersection of the lines xa+yb=1,xb+ya=1 meets the coordinate axes in A and B. Then the locus of the mid point of AB is

A
2xy(a+b)=ab(x+y)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
xy(a+b)=ab(xy)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
xy(a+b)=ab(x+y)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
xy(a+b)=2ab(x+y)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 2xy(a+b)=ab(x+y)
Let C be the point of intersection of the lines.
Then, C=(aba+b+aba+b)
Let M(h,k) be the mid- point of AB
Then, the equation of A may be written as x2h+y2k=1
Since AB passes through C, we have
ab2h(a+b)+ab2k(a+b)=11h+1k=2(a+b)ab
Therefore locus of M(h,k) is 1x+1y=2(a+b)ab
2xy(a+b)=ab(x+y)

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