The general equation xy = 1 is transformed into a parametric equation

The general equation xy = 1 is transformed into a parametric equation

In fact, X and y can take any value other than 0. Consider using trigonometric function as parameter equation,
x=tanα
y=1/tanα
It just satisfies this condition. α ∈ (0,2 π)

Write out the parameter equation of ellipse x ^ 2 + XY + y ^ 2 = 1

x=2√3/3*cosθ,
y=sinθ-√3/3*cosθ
Where 0

The perplexity about the parameter equation of space curve
|x=x(t)
|y=y(t)
|z=z(t)
Why does it represent a curve when there is only one parameter? Can't it represent a face? I think it's OK. And why does it represent a face when there are two parameters?

Halo, because whether it is a curve or a straight line, as long as you determine the coordinate axis of one, then that position is fixed. The other two axes can be calculated without depending on the other axis, but not necessarily for the surface. You need to determine two parameters to calculate the value of the third axis

The general equation of a curve is transformed into a parametric equation
x²+y²=1
Let x = Sint, y = cost,
Can we make x = cost, y = Sint

The parameterized equation itself is such that x = cost, y = Sint, because Sint = Y / R, cost = x / R, r = 1