Parabola

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A parabola is a curve where any point is at an equal distance from a fixed point (focus ), and a fixed straight line (directrix).

Parabola

$$y^2=2px$$

Equation of a translated parabola

$${\left(y-v\right)}^2=2p\left(x-u\right)$$

Tangency condition of a central parabola and a line

$$p=2·k·n$$

where the equation of the tangent line is: