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

Given A=(1,1) and AB is any line through it cutting the x-axis in B. if AC is perpendicular to AB and meets the y-axis in C, then the equation of locus of mid-point P of BC is

A
x+y=1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
x+y=2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
x+y=2xy
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
2x+2y=1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A x+y=1
Let (h,k) be the mid point on the line BC.
Equation of AB
(y1)=m(x1)
Since given that ABAC,
Therefore,
Equation of AC
(y1)=1m(x1)
Now, from fig.,
11m=2h
1m=12h.....(1)
Again from fig.,
1+1m=2k
1m=2k1.....(2)
From eqn(1)&(2), we have
12h=2k1
2(h+k)=2
h+k=1
Replacing h and k with x and y repectively, we hve
x+y=1
Hence the locus of mid-point of BCC is x+y=1
Hence the correct answer is (A)x+y=1.

1131954_1151821_ans_16d0e841e16a49a496fb57fe4fab98ac.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometric Representation and Trigonometric Form
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon