Question

Find the whole area included between the curve $x^2{y}^2=a^2(y^2-x^2)$ & its asymptotes (asymptotes are the lines which meet the curve at infinity).

Answer 1

$x^2{y}^2=a^2(y^2-x^2)$

$a^2(y^2-x^2)-x^2{y}^2=0$

Equating it to zero, coefficient of $x^2$

$a^2-y^2=0$

$y=\pm a\parallel xaxis$

similarly

$x=\pm a\parallel yaxis$

x coordinates when $y=\pm a$

$x^2=a^2-x^2$

$\Rightarrow$ $x=\pm \frac{a}{\sqrt{2}}$

similarly $y=\pm \frac{a}{\sqrt{2}}$

As we can see they form a square

$Area=[\sqrt{2a}{]}^2$

$\Rightarrow$ $2a^2$