Question

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

• A. A pair of lines
• B. Pair of lines and a circle
• C. A pair of lines and a parabola
• D. Four lines forming a square

Answer 1

The correct option is D Four lines forming a square

Collecting the terms $y^2$ and y the given equation can be written as
$y^2(x^2-2x-3)-4y(x^2-2x-3)=0$
or $(x-3)(x+1)y(y-4)=0$
It represents four lines $x=-1$, $x=3$, $y=0$ and $y=4$.
These two sets of parallel lines form a square of side four.