KVPY SX SB Exam 2013 Question Paper

Question : 5 of 120

Marks: +1, -0

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

$r^2={a^2+b^2}/4$
$r^2\cos2θ={a^2-b^2}/4$
$r^2=4(a^2+b^2)$
$r^2\cos2θ=4(a^2-b^2)$

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\cosθ

and

g^2-f^2={a^2-b^2}/4

f=-r\sinθ

∴r^2\sin θ={a^2-b^2}/4

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