# ELLIPSE | QUICK REVISION | JEE Main | JEE Advanced | BITSAT – By Nitesh Choudhary - Videos

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In this video, we will revise the topic ELLIPSE.

I will start the topic by discussing the general equation of ellipse i.e. how to find the equation given its focus and equation of directrix. It is defined as the locus of a point which moves in such a way that the ratio of its distance from a fixed point and a fixed line is constant (eccentricity), which is less than one. Then, we will discuss standard equations of ellipse (referred to its principal axes along the co-ordinate axes) x^2/a^2 + y^2/b^2 = 1 and x^2/b^2 + y^2/a^2 = 1 (where a is greater than b) and will define the major axis and minor axis of the ellipse.

Next, we will discuss important parameters related to the equation of the ellipse – 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, Centre of ellipse, Area of Ellipse. How to find the coordinate of any point on the ellipse whose distance from focus i.e. focal radius is given? An important property of ellipse is that, sum of focal distances of any point P on the ellipse is constant and is equal to the length of major axis. We will also discuss about auxiliary circle (a circle described on major axis of the ellipse as diameter) and eccentric angle. Then, we will discuss topics related to a point and an ellipse. What are the conditions that needs to be applied if the point lies inside the ellipse, on the ellipse or outside the ellipse?

Next discussion will be related to equation of tangent to an ellipse. First topic is, what is the condition to be applied given a line is tangent to an ellipse or line is chord to an ellipse – 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. The eccentric angles of the points of contact of two parallel tangents differ by π. Then, we will learn how to find the equation of tangents to an ellipse from an external point and angle between those tangents. Next is to find the locus of point of intersection of two perpendicular tangents i.e. Equation of Director Circle: x^2 + y^2 = a^2 + b^2. Then, we will discuss how to find the equation of pair of tangents to an ellipse. We will also some important results related to equation of tangents which are:
– The Locus Of Feet Of Perpendiculars From The Foci Upon Any Tangent Is Auxiliary Circle.
– The Product Of Perpendiculars From The Foci Upon Any Tangent Of The Ellipse Is b^2.
– The Length Of Tangent Between The Point Of Contact And The Point Where It Meets The Directrix Subtends Right Angle At The Corresponding Focus.
– The Tangents At The Extremities Of The Latus Rectum Of An Ellipse Intersect At The Foot Of The Corresponding Directrix And The Quadrilateral Thus Formed By Them Is A Rhombus Of Area: 2a^2/e.

Then, we will move onto discuss the equation of chord of an ellipse. In that, we will discuss the equation of chord and its slope in parametric form. Then, we will learn about some important properties related to focal chord – Semi-Latus Rectum is the harmonic mean of SP and SQ, where S is the focus and P, Q are the extremities of the focal chord. Then, we will discuss the equation of chord of contact and equation of chord with given middle point.

Next is the equation of normal to both the ellipses: x^2/a^2 + y^2/b^2 = 1 and x^2/b^2 + y^2/a^2 = 1 (where a is greater than b) – 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 ellipse.

We will conclude the discussion with the important reflection property of an ellipse – Rays Emanating From One Focus After Reflecting On The Ellipse Passes Through Other Focus And Vice Versa Is Also True.

By – Nitesh Choudhary
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https://www.instagram.com/coachengg

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Some Other Important Links are given below:

Mathematical Reasoning IIT JEE Lectures Playlist Link

Statistics IIT JEE Lectures Playlist Link

Sum of Series IIT JEE Concepts Playlist Link

Permutation and Combination IIT JEE Concepts Playlist Link

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1. TEJ PARTAP Singh

Thanks Bhai

2. Akhil 126

Sir when will u upload physics formulae videos?? Pls do it before mains sir. Helps a lot.

3. Kumkum Mishra

sir please !!upload a video on sequence and series -(common terms questions and coefficient of x to the power type questions )

4. Bhavesh Jaglan

5. 24/7 News

6. manish pandey

thanks sir

7. Dragon Ball Onplay

thank you so much ..I really needed that !!!

8. Shubham Sagar

sir how find eccentricity when focal radio makes 90 angle at ellipse

9. Rohit Kumar

Sir hyperbola ka ek video banaiye pls its the toughest one

10. Ritesh Sharma

sir plzz upload a revision session on ray optics…physics is just like a nightmare so plzz help me to learn concepts of ray optics…

11. lovepreet singh

sir very very thankyou for this. It was soo dificult to revise this topic but now with this video it become easy. And plz some make more video on other topics. once again thankyou sir.

12. ASHWANI KUMAR

mains me sir ,, tangent ke aage bhi h kya

13. ghana shyam

sir do for hyperbola too

14. Abhijit Gupta

hyperbola plzz

15. Abhijit Gupta

and some past year question set on conics …

16. Pratyush Gour

17. Rahul Raj

thank u so much sir for this video but I need straight line revision video plz make video sir becoz as we know it is easy and from this chapter one question surely come

18. Living Legend

u r GOD

19. S.Kavin Balaji

thank u so much for this

20. Shubham Sagar

sir.there's a question…Q.focus of an ellipse is at the origin.the directrix is the line x=4 and the eccentricity is 1/2.then the length of semi major axis is…….
(Aieee-2008)

21. Mayank Rai

sir properties

22. Geeky Geek

23. Ravi Tanwani
24. Ankit Kumar
25. grow_up_ boron