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UPSC NDA I 2016 Mathematics Solved Paper
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© examsnet.com
Question : 8
Total: 120
If a circle of radius b units with centre at (0,b) touches the line
y
=
x
−
√
2
,then what is the value of b ?
[NDA I 2016]
2
+
√
2
2
−
√
2
2
√
2
√
2
Validate
Solution:
Distance from the center to the point of line which touches circle is OM = radius
r
=
|
A
x
0
+
B
y
0
+
C
|
√
A
2
+
B
2
∵
x
0
=
0
&
Y
0
=
b
b
=
|
1
(
0
)
+
(
−
1
)
(
b
)
−
√
2
|
√
(
1
)
2
+
(
−
1
)
2
b
=
b
+
√
2
√
2
(
√
2
−
1
)
b
=
√
2
⇒
b
=
2
+
√
2
© examsnet.com
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