1.0 Conic Section

  Parabola

The locus of a point which moves in a plane such that the ratio of its distance from a fixed point to its perpendicular distance from a straight line is always constant is known as Conic Section or a conic. The fixed point is called the focus of the conic and the fixed line is called the directrix of the conic. This constant ratio is called the eccentricity of the conic denoted by $e$.

• If $e=1$, the conic is a parabola.
• If $e<1$, the conic is an ellipse.
• If $e>1$, the conic is a hyperbola.
• If $e=0$, the conic is a circle.
• If $e=\infty $, the conic is the pair of straight lines.

As shown in figure $1$,

$$\frac{{SP}}{{PM}} = {\text{constant}} = e$$ $$SP = e \times PM$$