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The equation

 \mathrm{x^2 y^2-2 x y^2-3 y^2-4 x^2 y+8 x y+12 y=0} represents

 

Option: 1

a pair of straight lines

 


Option: 2

a pair of straight lines and a circle

 


Option: 3

a pair of straight lines and a parabola

 


Option: 4

a set of four lines forming a square


Answers (1)

best_answer

\mathrm{\begin{array}{ll} x^2 y^2-2 x y^2-3 y^2-4 x^2 y+8 x y+12 y & =y^2\left(x^2-2 x-3\right)-4 y\left(x^2-2 x-3\right)=0 \\ \Rightarrow y(y-4)(x-3)(x+1)=0 & \Rightarrow y=0, y=4, x=3, x=-1 \end{array}}

Hence the equation represents four straight lines which evidently form a square.

Hence correct answer is (d).

 

Posted by

Gautam harsolia

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