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Byju's Answer
Standard XII
Mathematics
Distance between Parallel Lines
Find the dist...
Question
Find the distance between the lines
3
x
+
4
y
=
9
and
6
x
+
8
y
=
15
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Solution
Solution:-
L
1
:
3
x
+
4
y
=
9
Here,
a
=
3
,
b
=
4
,
c
1
=
−
9
L
2
:
6
x
+
8
y
=
15
⇒
3
x
+
4
y
=
15
2
Here,
a
=
3
,
b
=
4
,
c
2
=
−
15
2
As we know that, distance between the two lines
L
1
:
a
x
+
b
y
+
c
1
=
0
and
L
2
:
a
x
+
b
y
+
c
2
=
0
is
d
=
|
c
2
−
c
1
|
√
a
2
+
b
2
∴
distance between the given lines,
(
d
)
=
∣
∣
∣
(
−
15
2
)
−
(
−
9
)
∣
∣
∣
√
3
2
+
4
2
⇒
d
=
∣
∣
∣
(
−
15
+
18
2
)
∣
∣
∣
√
25
⇒
d
=
(
3
2
)
5
⇒
d
=
3
10
Hence, the distance between the lines
3
x
+
4
y
=
9
and
6
x
+
8
y
=
15
is
3
10
units.
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Similar questions
Q.
The distance between the lines
3
x
+
4
y
=
9
and
6
x
+
8
y
=
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is
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=
9
and
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x
+
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15
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