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Byju's Answer
Standard XII
Mathematics
Distance between Parallel Lines
The distance ...
Question
The distance between two straight lines
y
=
m
x
+
c
1
and
y
=
m
x
+
c
2
is
|
c
1
−
c
2
|
. Then the value of
m
is
A
1
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B
−
1
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C
0
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D
none of these
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Solution
The correct option is
C
0
Given
the distance between two straight lines
y
=
m
x
+
c
1
....(1) and
y
=
m
x
+
c
2
is
|
c
1
−
c
2
|
.....(2).
Now we have the distance between the two lines is
∣
∣
∣
c
1
−
c
2
√
1
+
m
2
∣
∣
∣
.
According to the problem,
|
c
1
−
c
2
|
=
∣
∣
∣
c
1
−
c
2
√
1
+
m
2
∣
∣
∣
or,
√
1
+
m
2
=
±
1
or,
1
+
m
2
=
1
or,
m
2
=
0
or,
m
=
0
.
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0
Similar questions
Q.
The distance between the straight lines
y
=
m
x
+
c
1
,
y
=
m
x
+
c
2
is
|
c
1
−
c
2
|
, then
m
=
Q.
The distance between the lines y = mx + c
1
and y = mx + c
2
, is
(a)
c
1
-
c
2
1
+
m
2
(b)
c
1
-
c
2
1
+
m
2
(c)
c
2
-
c
1
1
+
m
2
(d)
c
1
-
c
2
Q.
If three lines whose rquation are
y
=
m
1
x
+
c
1
,
y
=
m
2
x
+
c
2
and
y
=
m
2
x
+
c
2
concurrent, then show that
m
1
(
c
2
−
c
1
)
+
m
2
(
c
3
−
c
1
)
+
m
3
(
c
1
−
c
2
)
=
0
Q.
m
≡
a
1
x
+
b
1
y
+
c
1
=
0
and
l
≡
a
2
x
+
b
2
y
+
c
2
=
0
are two straight lines such that
a
1
a
2
=
b
1
b
2
=
c
1
c
2
then
m
+
k
l
=
0
,
k
∈
R
is :
Q.
Consider two curves
C
1
:
y
=
1
x
and
C
2
:
y
=
l
n
x
on the xy plane Let
D
1
denotes the region surrounded by
C
1
,
C
2
and the line
x
=
1
and
D
2
denotes the region surrounded by
C
1
,
C
2
and the line
x
=
a
If
D
1
=
D
2
then the value of 'a':
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