# Parabola

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

$$p=2\xb7k\xb7n$$

where the equation of the tangent line is:

$$y=kx+n$$

Keywords: parabola, central parabole, equation of a parabola, tangent to a parabola