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Byju's Answer
Standard XI
Mathematics
Pair of lines
Find the equa...
Question
Find the equations to the straight lines passing through the point (2, 3) and inclined at and angle of 45° to the line 3x + y − 5 = 0.
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Solution
We know that the equations of two lines passing through a point
x
1
,
y
1
and making an angle
α
with the given line y = mx + c are
y
-
y
1
=
m
±
tan
α
1
∓
m
tan
α
x
-
x
1
Here,
Equation
of
the
given
line
is
,
3
x
+
y
-
5
=
0
⇒
y
=
-
3
x
+
5
Comparing
this
equation
with
y
=
m
x
+
c
we
get
,
m
=
-
3
x
1
=
2
,
y
1
=
3
,
α
=
45
∘
,
m
=
-
3
.
So, the equations of the required lines are
y
-
3
=
-
3
+
tan
45
∘
1
+
3
tan
45
∘
x
-
2
and
y
-
3
=
-
3
-
tan
45
∘
1
-
3
tan
45
∘
x
-
2
⇒
y
-
3
=
-
3
+
1
1
+
3
x
-
2
and
y
-
3
=
-
3
-
1
1
-
3
x
-
2
⇒
y
-
3
=
-
1
2
x
-
2
and
y
-
3
=
2
x
-
2
⇒
x
+
2
y
-
8
=
0
and
2
x
-
y
-
1
=
0
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Similar questions
Q.
Find the equations to the straight lines passing through the point (3, −2) and inclined at 60° to the line
3
x
+
y
=
1
.
Q.
Show that the equations to the straight lines passing through the point
(
3
,
−
2
)
and inclined at
60
o
to the line
√
3
x
+
y
=
1
are
y
+
2
=
0
and
y
−
√
3
x
+
2
+
3
√
3
=
0
.
Q.
Find the equations of the straight lines passing through the point
(
−
3
,
2
)
and making an angle of
45
t
h
with the straight line
3
x
−
y
+
4
=
0
.
Q.
Find the equation to the straight line which passes through the point (3, -2) and inclined at
60
o
to the line
√
3
x
+
y
=
1
Q.
The axes being inclined at an angle of
30
o
, find the equation to the straight line which passes through the point
(
−
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,
3
)
and is perpendicular to the straight line
y
+
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x
=
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.
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