The equation of a curve is $\displaystyle x^2y^2-x^2+y^2=0$

a) find the equation of the tangents at the origin

b) find the equations of the real asymptotes

c) show that the numerical value of y is never greater than the corresponding value of x

d)show that the numerical value of y is always less than unity

My problem is with (c) and (d). I've done (a) and (b) already.

For (c), $\displaystyle x-y\geq 0$

$\displaystyle y=\pm\frac{x}{\sqrt{x^2+1}}$

Substitute

$\displaystyle x-\frac{x}{\sqrt{x^2+1}}=\frac{x\sqrt{x^2+1}-x}{\sqrt{x^2+1}}$

Now I don't know how to continue to make it such that it is greater or equal to 0, which then i can show that y is always lesser of equal to x.

Same problem with the next one. The $\displaystyle \sqrt{x^2+1}$ is what stumble me.

Thanks!