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Byju's Answer
Standard X
Mathematics
Equation of a Line Parallel to a Straight Line
Find the equa...
Question
Find the equation of the line equidistant from the point (2,-2) and the line 3x-4y+1=0
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Solution
The
line
which
is
equidistant
from
point
(
2
,
-
2
)
and
3
x
-
4
y
+
1
=
0
mmust
be
parallel
to
3
x
-
4
y
+
1
=
0
.
i
,
e
,
equation
of
reqd
line
is
3
x
-
4
y
+
c
=
0
Now
,
perpendicular
distance
from
(
2
,
-
2
)
=
Ax
+
By
+
c
A
2
+
B
2
=
3
×
2
-
4
(
-
2
)
+
c
3
2
+
4
2
=
14
+
c
5
distance
between
the
lines
=
c
1
-
c
2
A
2
+
B
2
=
1
-
c
5
Now
,
14
+
c
5
=
1
-
c
5
⇒
14
+
c
=
1
-
c
⇒
c
=
-
13
2
Thus
,
required
line
:
3
x
-
4
y
-
13
2
=
0
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