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TS EAMCET 20-July-2022 Shift 1 Solved Paper
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© examsnet.com
Question : 42
Total: 160
A line makes intercepts 5 and 7 on the coordinate axes. The axes are rotated through an angle
θ
in the positive direction about the origin so that the line makes equal intercepts on the new axes, then
|
tan
θ
|
=
6
1
6
12
35
35
12
Validate
Solution:
👈: Video Solution
x
-intercept of line
=
5
So,
a
=
5
(
5
,
0
)
.
y
-intercept of line
=
7
So,
b
=
7
(
0
,
7
)
Equation of line :
x
a
+
y
b
=
1
⇒
x
5
+
y
7
=
1
Equation of line w.r.t. old axis :
7
x
+
5
y
=
35
Now replace
x
→
x
cos
θ
−
y
s
i
n
θ
,
y
→
x
s
i
n
θ
+
y
cos
θ
Equation of line
L
w.r.t. new axis
7
(
x
cos
θ
−
y
s
i
n
θ
)
+
5
(
x
s
i
n
θ
+
y
cos
θ
)
=
35
(
7
cos
θ
+
5
s
i
n
θ
)
x
+
(
5
cos
θ
−
7
s
i
n
θ
)
y
=
35
For
x
-intercept, on putting
x
=
0
,
x
-intercept
=
35
7
cos
θ
+
5
s
i
n
θ
For
y
-intercept, on putting
x
=
0
,
y
-intercept
=
35
5
cos
θ
−
7
s
i
n
θ
Given,
x
-intercept
=
y
-intercept
∴
7
cos
θ
+
5
s
i
n
θ
=
5
cos
θ
−
7
s
i
n
θ
⇒
tan
θ
=
−
1
6
∴
|
tan
θ
|
=
1
6
© examsnet.com
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