Question

Find asymptotes of the curve x^2y^2=a^2(x^2+y^2)

Answer 1

Step-by-step explanation:

x2y2=a2(y2−x2)

a2(y2−x2)−x2y2=0

Equating it to zero, coefficient of x2

a2−y2=0

y=±a∥xaxis

similarly

x=±a∥yaxis

x coordinates when y=±a

x2=a2−x2

⇒   x=±2a

similarly  y=±2a

As we can see they form a square

Area=[2a]2

⇒    2a2