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Test Index
TS EAMCET 19-July-2022 Shift 2 Solved Paper
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© examsnet.com
Question : 43
Total: 160
If a straight line
L
passing through the point
(
5
,
−
3
)
is inclined at an angle of
60
∘
to the line
√
3
x
+
y
−
9
=
0
and
L
intersects
X
-axis then the equation of
L
is
x
−
√
3
y
−
3
−
5
√
3
=
0
√
3
x
−
y
−
3
−
5
√
3
=
0
√
3
x
−
y
+
3
+
5
√
3
=
0
x
−
√
3
y
+
3
+
5
√
3
=
0
Validate
Solution:
Let the line
L
intersect
X
-axis at a point
(
h
,
0
)
.
Slope of line
L
(
m
1
)
=
0
+
3
h
−
5
=
3
h
−
5
Slope of line
(
m
2
)
,
√
3
x
+
y
−
9
=
0
is
−
√
3
tan
60
∘
=
|
3
h
−
5
+
√
3
1
−
3
√
3
h
−
5
|
⇒
√
3
=
|
3
+
√
3
(
h
−
5
)
h
−
5
−
3
√
3
|
⇒
√
3
=
±
3
+
√
3
(
h
−
5
)
h
−
5
−
3
√
3
When
√
3
=
3
+
√
3
(
h
−
5
)
h
−
5
−
3
√
3
⇒
√
3
h
−
5
√
3
−
9
=
3
+
√
3
h
−
5
√
3
(Not possible)
When
√
3
=
−
(
3
+
√
3
(
h
−
5
)
)
h
−
5
−
3
√
3
⇒
√
3
h
−
5
√
3
−
9
=
−
3
−
√
3
h
+
5
√
3
⇒
2
√
3
h
=
10
√
3
+
6
⇒
h
=
5
+
√
3
The line
L
intersect
X
-axis at point
(
5
+
√
3
,
0
)
. Equation of line
L
is
y
+
3
=
3
√
3
(
x
−
5
)
⇒
y
+
3
=
√
3
(
x
−
5
)
⇒
√
3
x
−
y
−
5
√
3
−
3
=
0
© examsnet.com
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