Question

The equation $x^2{y}^2-9y^2-6x^{2}y+54y=0$ represents

• A. A pair of straight lines and a circle
• B. A pair of straight lines and a parabola
• C. A set of four straight lines forming a square
• D. None of these

Answer 1

Answer: (C)

A set of four straight lines forming a square

$x^2{y}^2-9y^2-6x^{2}y+54y=0$
$y^2(x^2-9)-6y(x^2-9)=0$
$(y^2-6y)(x^2-9)=0$
$y(y-6)(x+3)(x-3)=0$
Therefore the lines are
$y=0$
$y=6$
$x=3$
$x=-3$
The above set of lines represent a square of side $6$ units.