Why no angle is involved in parametric equation of parabola?

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Why only in parametric equation of parabola, angle is not involved unlike parametric equation in ellipse and hyperbola, angle is involved. Thank you.

[edit]:

In parametric equation of parabola $y^2=4ax$, any coordinate on the parabola is taken as ($at^2,2at$).

$t$ is not an angle here.

Where as in ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2}$$ it is ($a\cos(t), b\sin(t)$), $t$ is not the angle made on the ellipse but on the circle of radius $a$.

Similarly on a hyperbola $$\frac{x^2}{a^2} - \frac{y^2}{b^2}$$ it is ($a\sec t,\pm b\tan t$)