Parabola

Parabola. Focus. Directrix. Equation of parabola.

Equation of tangent line to parabola.

Tangency condition of straight line and parabola.

A parabola ( Fig.1 ) is called a locus of points, equidistant from the given point  F , called a focus of parabola, and the given straight line, not going through this point

and called a directrix of parabola.

An equation of parabola ( Fig.1 ) is :

                                                                                   y ² = 2 p x .

The axis ОХ  is here an axis of symmetry of parabola.

Let  Р ( х₁ ,  у ₁ )  be a point of parabola, then an equation of tangent line to parabola in this point is : 

                                                                              у ₁ y  = p ( x +  х₁ ) .          

A tangency condition of a straight line  y = m x + k and a parabola  y ² = 2 p x : 

                                                                                 2 m k  = p .

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