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A parabola is a set of all points in a plane that are equidistant from a given fixed point (the Focus) and a given straight line (the Directrix).


Algebraic equation
x^2 - 4ya = 0

Cartesian equation
y = \frac{x^{2}}{4a}

Parametric equations
x(t) = 2 t a
y(t) = t^2 a

Polar equation
r(\theta) = 4 tan(\theta) sec(\theta) a

Differential equation
3y'(x) y'' (x^{2})-y^{3}(x)y'(x^{2}) =0