KVPY SB SX Exam 2011 Question Paper

Question : 5 of 120

Marks: +1, -0

All the points (x, y) in the plane satisfying the equation

x^2 + 2x \sin(xy) + 1 = 0

lie on

Solution:

x^2 + 2 x \sin (xy) + 1 = 0

2\sin (xy)=-(x+1/x)

\table {\R.\H.\S} ≥ 2 ,\or ,≤ 2;⇓,,⇓;\L.\H.\S= {\R.\H.\S}=2,,\sin(xy)=-1;⇓,,(x=1);x=-1;\sin(-y)=1,,\sin y=-1;\sin y=-1

y=2nπ-π/2,n ∈ I

Hence pair of straight lines.

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