Question

The equation $x^2{y}^2-2x{y}^2-3y^2-4x^{2}y+8xy+12y=0$ represents

• A. a pair of straight lines
• B. a pair of straight lines and a circle
• C. a pair of straight lines and a parabola
• D. a set of four lines forming a square

Answer 1

The correct option is D a set of four lines forming a square

Given equation is

$x^2{y}^2-{2xy}^2-{3y}^2-{4x}^{2}y+8xy+12y=0$

$\Rightarrow y^2(x^2-2x-3)-4y(x^2-2x-3)=0$

$\Rightarrow y(y-4)(x-3)(x+1)=0$

$\Rightarrow y=0,y=4,x=3,x=-1$

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