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KVPY SX SB Exam 2012 Question Paper
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© examsnet.com
Question : 4
Total: 120
Suppose two perpendicular tangents can be drawn from the origin to the circle
x
2
+
y
2
−
6
x
−
2
p
y
+
17
=
0
, for some real p. Then |p| is equal to
0
3
5
17
Validate
Solution:
(
x
−
3
)
2
+
(
y
−
p
)
2
=
9
−
17
+
p
2
Director circle is
(
x
−
3
)
2
+
(
y
−
p
)
2
=
2
(
p
2
−
8
)
Passes through (0, 0)
9
+
p
2
=
2
p
2
−
16
p
2
=
25
⇒
p
=
±
5
⇒
|
p
|
=
5
© examsnet.com
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