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JEE Main Math Class 11 Straight Lines and Pair of Straight Lines 1 Questions
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© examsnet.com
Question : 4
Total: 100
A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is
1
4
. Three stones
A
,
B
and
C
are placed at the points
(
1
,
1
)
,
(
2
,
2
)
and
(
4
,
4
)
respectively. Then which of these stones is\/are on the path of the man?
24 Feb 2021 Shift 1
A only
C
only
All the three
B only
Validate
Solution:
Let the line be
y
=
m
x
+
c
∴
x
-intercept
:
−
c
m
y
-intercept :
c
A.M. of reciprocals of the intercepts :
−
m
c
+
1
c
2
=
1
4
⇒
2
(
1
−
m
)
=
c
Line :
y
=
m
x
+
2
(
1
−
m
)
=
c
⇒
(
y
−
2
)
−
m
(
x
−
2
)
=
0
⇒
line always passes through
(
2
,
2
)
© examsnet.com
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