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KEAM 2010 Math Paper
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© examsnet.com
Question : 115
Total: 120
The slopes of the lines which make an angle
45
∘
with the line
3
x
−
y
=
−
5
are
1,-1
1
2
,
−
1
1
,
1
2
2
,
−
1
2
−
2
,
1
2
Validate
Solution:
The slope of line
3
x
−
y
=
−
5
is
m
1
=
3
∴ The slope of required line is
=
m
1
±
tan
45
∘
1
∓
m
1
⋅
tan
45
∘
=
3
±
1
1
∓
3
⋅
1
=
−
2
,
1
2
Alternate
Given line
3
x
−
y
=
−
5
m
1
=
3
Let slope of another line
=
m
2
Now, angle between both the lines
tan
θ
=
|
m
1
−
m
2
1
+
m
1
m
2
|
tan
45
∘
=
m
1
−
m
2
1
+
m
1
m
2
or
m
2
−
m
1
1
+
m
1
m
2
(If
m
1
>
m
2
)
⇒
1
+
m
1
m
2
=
m
1
−
m
2
⇒
1
+
3
m
2
=
3
−
m
2
⇒
m
2
=
1
2
(If
m
2
>
m
1
)
Then,
1
+
3
m
2
=
m
2
−
3
⇒
m
2
=
−
2
© examsnet.com
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