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 ну is here an axis of symmetry of parabola.
Let п ( У 1 , С 1 ) be a point of parabola, then an equation of tangent line to parabola in this point is :
С 1 y = p ( x + У 1 ) .
A tangency condition of a straight line y = m x + k and a parabola y 2 = 2 p x :
2 m k = p .