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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  is here an axis of symmetry of parabola.

 

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

 

                                                                              1 y  = p ( x +  1 ) .          

 

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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