KVPY 2013 - 5

Geometry Level 4

Two line segments A B AB and C D CD are constrained to move along the x x and y y axes respectively, in such a way that the points A , B , C , D A,B,C,D are concyclic .

If A B = a AB=a and C D = b CD=b , then the locus of the centre of the circle passing through A , B , C , D A,B,C,D in polar coordinates is?

Try the whole set KVPY 2013 SB/SX here.

r 2 = a 2 + b 2 4 r^2=\dfrac{a^2+b^2}{4} r 2 c o s 2 θ = a 2 − b 2 4 r^2cos2\theta=\dfrac{a^2-b^2}{4} r 2 = 4 ( a 2 + b 2 ) r^2=4(a^2+b^2) r 2 c o s 2 θ = 4 ( a 2 − b 2 ) r^2cos2\theta=4(a^2-b^2)

Skanda Prasad by Skanda Prasad , 20, India

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