I can't figure out how to convert this function to parametric form.
$$\ x^4 – y^4 = xy$$
$$\ x(t) =? $$
$$\ y(t) =? $$
Any help would be greatly appreciated. Thanks!
parametric
I can't figure out how to convert this function to parametric form.
$$\ x^4 – y^4 = xy$$
$$\ x(t) =? $$
$$\ y(t) =? $$
Any help would be greatly appreciated. Thanks!
Best Answer
Observe,
$$(x^2+y^2)(x^2-y^2) = xy\tag{1}$$
and let
$$x(t)=z(t)\cos t, \>\>\>\>\>y(t)=z(t)\sin t$$
Then, plug above form into (1) to obtain $z(t) = \frac{1}{\sqrt2}\sqrt{\tan 2t}$. Thus, the parametrized expressions are,
$$x(t)=\frac {1}{\sqrt2}\cos t\sqrt{\tan 2t} $$
$$y(t)=\frac {1}{\sqrt2}\sin t\sqrt{\tan 2t} $$