# Parabola

**Importance**

A parabola represents the locus of all points moving such that its distance from a fixed line, directrix and its distance from a fixed point, focus is equal. The equation of standard parabola is !!y^2=4ax!! having !!x-!! axis as its axis.

**Yearly Trend**

You can easily expect a question or two from the chapter as the number of concepts are more, plus the topic can be related with various other topics such as circles and ellipse and straight lines.

Let us have a look on important topics of parabola.

**Topics**

Like any other chapter in the Conics section, **parametric coordinates** lying on the curve is a really important concept.

For the standard parabola, !!y^2=4ax!!,he prametric coordinates are given by !!(at^2,2at)!!

**Tangent**: Application of various properties related to the tangent of a parabola have been asked repeatedly. Various forms of equation of tangent are there, slope form, parametric form, point form, better get a hang of all these forms. The equation for tangent to the parabola in parametric form is given by :
!!ty=x+at^2!!.

**Normal**: Normal is a topic which is somewhat related to tangent. The questions asked are based on the properties and various forms of the equation of normal are there. The equation of normal in slope form for parabola !!y^2=4ax!! is !!y=mx-2am-am^3!!.

Then come the concepts of **chord of contact, latus rectum**. Questions are asked from these concepts as well.

Also, try and remember the very definition of parabola, a very complex two degree equation might be a hidden parabola in the form of distance of a point from a line and a point. This thing is true for every conic.