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EAMCET Engineering 2005 Solved Paper
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© examsnet.com
Question : 135
Total: 160
If
y
=
3
x
is a tangent to a circle with centre
(
1
,
1
)
, then the other tangent drawn through
(
0
,
0
)
to the circle is
3
y
=
x
y
=
−
3
x
y
=
2
x
y
=
−
2
x
Validate
Solution:
Since the line
y
−
3
x
=
0
touches the circle
∴
radius
=
perpendicular distance from the centre
(
1
,
1
)
to the tangent
=
|
1
−
3
|
√
1
+
9
=
2
√
10
. . . (i)
Let the other equation of tangent which is passing through origin is
y
=
m
x
.
radius
=
|
1
−
m
|
√
1
+
m
2
⇒
4
10
=
(
1
−
m
)
2
(
1
+
m
2
)
⇒
2
(
1
+
m
2
)
=
5
(
1
+
m
2
−
2
m
)
⇒
3
m
2
−
10
m
+
3
=
0
⇒
3
m
2
−
9
m
−
m
+
3
=
0
⇒
(
3
m
−
1
)
(
m
−
3
)
=
0
⇒
m
=
3
,
1
3
at
m
=
3
,
y
=
3
x
it is already given.
at
m
=
1
3
,
3
y
=
x
© examsnet.com
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