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TS EAMCET 04 May 2019 Shift 1 Solved Paper
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© examsnet.com
Question : 49
Total: 160
A line meets the coordinate axes at A and B. If the perpendicular distances from A and B to the tangent drawn at the origin to the circumcircle of ΔOAB are m and n respectively, then the diameter of that circle is
m
+
n
2
3
(
m
+
n
)
4
m + n
2 (m + n)
Validate
Solution:
The equation of the circle passing through
(
a
,
0
)
and
(
0
,
b
)
and(0,0) is,
x
2
+
y
2
−
a
x
−
b
y
=
0
Consider the diagram,
Equation of the tangent at origin is given by,
a
x
+
b
y
=
0
P
A
=
a
2
√
a
2
+
b
2
This implies,
m
=
|
a
2
√
a
2
+
b
2
|
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
(
I
)
And
B
Q
=
n
=
|
b
2
√
a
2
+
b
2
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
(
I
I
)
|
This implies,
m
2
+
n
2
=
a
4
+
b
4
a
2
+
b
2
And,
m
n
=
a
2
b
2
a
2
+
b
2
Now
m
2
+
n
2
+
2
m
n
=
a
4
+
b
4
+
2
a
2
b
2
a
2
+
b
2
(
m
+
n
)
2
=
(
a
2
+
b
2
)
2
a
2
+
b
2
=
a
2
+
b
2
So, the diameter of circle is given by.
d
=
√
a
2
+
b
2
=
√
(
m
+
n
)
2
=
m
+
n
© examsnet.com
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