COACHengg App Download Link:
https://play.google.com/store/apps/de...

Share this Video Spread Learning
Link to share:    • PARABOLA | QUICK REVISION | JEE Main ...  
__________________________________________________________________________________

In this video, we will revise the topic PARABOLA.

I will start the topic by discussing the general equation of parabola i.e. how to find the equation given its focus and equation of directrix. Then, we will discuss standard equation of parabola y^2 = 4ax and x^2 = 4ax and important parameters related to it – coordinates of focus, equation of directrix, focal chord, double ordinate, focal radii, latus rectum (shortest focal chord), Length of latus rectum, End points of latus rectum, Parametric form. How to find the coordinate of any point on the parabola whose distance from focus i.e. focal radius is given. We will also discuss general equation of the parabola whose axis is either parallel to xaxis or parallel to yaxis.

Next, we will discuss topics related to a point and a parabola. What are the conditions that needs to be applied if the point lies inside the parabola, on the parabola or outside the parabola.

Next discussion will be related to equation of tangent to a parabola. First topic is, what is the condition to be applied given a line is tangent to a parabola or line is chord to a parabola – slope form of tangent. How to find the equation of a tangent, point of contact on circle is given i.e. point form of tangent. We will also discuss equation of tangent in parametric form and the point of intersection of two tangents.

We will discuss an important property that xcoordinate of point of intersection is geometric mean of xcoordinates of point of contacts and ycoordinate of point of intersection is arithmetic mean of ycoordinates of point of contacts. What is the condition between parameters t1 and t2, if two tangents are perpendicular? How to find the locus of point of intersection of two perpendicular tangents i.e. Directrix. How to find the angle between tangents drawn from the external point. How to find the area of the triangle formed by pair of tangents and the chord of contact. How to find the length and equation of the chord of contact to a parabola and also the equation of pair of tangents.

Then, we will move onto discuss the equation of chord of a parabola. In that, we will discuss the equation of chord and its slope in parametric form. What is the condition between parameters t1 and t2 such that the chord subtends right angle at the vertex of the parabola. We will also various properties related to focal chord condition between parameters t1 and t2, length of focal chord in terms of t1 and t2, length of focal chord if its angle with axis is given, SemiLatus Rectum is the harmonic mean of SP and SQ, where S is the focus and P, Q are the extremities of the focal chord, Circle taking focal chord PQ as diameter touches the directrix, Point of intersection of tangents at the end points of focal chord lies on directrix.

Next, we will two important properties related to focal radii.

First property Circle taking focal radius PS as diameter touches the tangent at vertex or Locus Of Foot Of Perpendicular From Focus Upon Any Tangent is Tangent At Vertex.
Second Property Length Of Tangent Between Point Of Contact (P) And Point Where It Meets The Directrix (Q) Subtends Right Angle At The Focus.
Then, we will discuss equation with given middle point.

Next is the equation of normal to both the parabolas y^2 = 4ax and x^2 = 4ay – Slope form, Point Form and Parametric Form. We will discuss the condition that need to be applied such a given line is normal to a parabola.

We will also discuss some important properties related to equation of normal – Relation between parameters t1 and t2 such that the normal at point P meets parabola again at Q, Normal other than axis of parabola never passes through focus (a, 0), Maximum 3 normal can be drawn from external point.
How to find the equation of normals to the given parabola from an external point.

We will conclude the discussion with the important property of parabolic reflector Any Line Parallel To The Axis Of The Parabola Passes Through Focus After Reflecting On The Parabola And Vice Versa Is Also True.

By – Nitesh Choudhary
__________________________________________________________________________________
Visit our facebook page
  / coachenggg  

Follow us on INSTAGRAM
  / coachengg  

Follow us on Google Plus
https://plus.google.com/+coachengg4u

_________________________________________________________________________________
Some Other Important Links:

Mathematical Reasoning IIT JEE Lectures Playlist Link
   • Playlist  

Statistics IIT JEE Lectures Playlist Link
   • Playlist