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KVPY SX SB Exam 2013 Question Paper
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© examsnet.com
Question : 5
Total: 120
Two line segments AB and CD are constrained to move along the x and y axes, respectively, in such a way that the points A ,B,C ,D are concyclic. If AB = a and CD = b , then the locus of the centre of the circle passing through A ,B,C ,D in polar coordinates is
r
2
=
a
2
+
b
2
4
r
2
cos
2
θ
=
a
2
−
b
2
4
r
2
=
4
(
a
2
+
b
2
)
r
2
cos
2
θ
=
4
(
a
2
−
b
2
)
Validate
Solution:
2
√
g
2
−
c
=
a
2
√
f
2
−
c
=
b
Polar coordinates of centre of circle be (r cosθ, r sinθ)
g
=
−
r
cos
θ
and
g
2
−
f
2
=
a
2
−
b
2
4
f
=
−
r
sin
θ
∴
r
2
sin
θ
=
a
2
−
b
2
4
© examsnet.com
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