Notes | EduRev

JEE Main Mock Test Series 2020 & Previous Year Papers

Created by: Learners Habitat

JEE : Notes | EduRev

The document Notes | EduRev is a part of the JEE Course JEE Main Mock Test Series 2020 & Previous Year Papers.
All you need of JEE at this link: JEE
  • The standard equation of ellipse with reference to its principal axis along the coordinate axis is given by x2/a+ y2/b2 = 1
  • In the standard equation, a >b and b2 = a2 (1-e2) Hence, the relation between a and b is a2 – b2 = a2e2, where ‘e’ is the eccentricity and 0 < e < 1.
  • The foci of the ellipse are S(ae, 0) and S’ = (-ae, 0) Notes | EduRev
  • Equations of the directrices are given by x = a/e and x = -a/e
  • The coordinates of vertices are A’ = (-a, 0) and A = (a,0)
  • The lengths of the major and minor axis are 2a and 2b respectively.
  • The length of latus rectum is 2b2/a = 2a(1-e2)
  • The sum of the focal distances of any pint on the ellipse is equal to the major axis. As a result, the distance of focus from the extremity of a minor axis is equal to semi major axis.
  • If a question does not mention the relation between a and b then by convention a is assumed to be greater than b i.e. a > b.
  • The point P(x1, y1) lies outside, inside or on the ellipse according as x12/a2 + y12/b– 1>< or = 0.
  • In parametric form, the equations x = a cos θ and y = b sin θ together represent the ellipse.
  • The line y = mx + c meets the ellipse x2/a2 + y2/b2 = 1 in either two real, coincident or imaginary points according to whether c2 is < = or > a2m+ b2
  • The equation y = mx + c is a tangent to the ellipse if c2 = a2m2+ b2
  • The equation of the chord of ellipse that joins two points with eccentric angles α and β is given byx/acos (α + β)/2 + y/b sin (α + β)/2 = cos (α - β)/2
  • The equation of tangent to the ellipse at the point (x1, y1) is given byxx1/a2 + yy1/b2 = 1
  • In parametric form, (xcosθ) /a + (ysinθ/b) is the tangent to the ellipse at the point (a cos θ a, b sin θ)
  • Equation of normal
    1. Equation of normal at the point (x1,y1) is
    a2x/x1 – b2y/y1 = a2- b2 = a2e2
    2.Equation of normal at the point (a cos θ a, b sin θ) is ax secθ – by cosec θ = (a2-b2)
    3. Equation of normal in terms of its slope ‘m’ is
    y = mx – [(a2-b2)m /√a2+b2m2]
  • The equation of director circle is x2+ y2= a2 + b
  • The portion of the tangent to an ellipse between the point of contact and the directrix subtends a right angle at the corresponding focus.
    The perpendiculars from the center upon all chords which join the ends of any particular diameters of the ellipse are of constant length.
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Complete Syllabus of JEE

JEE

Dynamic Test

Content Category

Related Searches

Objective type Questions

,

Sample Paper

,

Free

,

pdf

,

practice quizzes

,

Notes | EduRev

,

mock tests for examination

,

Exam

,

shortcuts and tricks

,

Previous Year Questions with Solutions

,

Notes | EduRev

,

Notes | EduRev

,

study material

,

Summary

,

video lectures

,

past year papers

,

MCQs

,

Important questions

,

ppt

,

Extra Questions

,

Semester Notes

,

Viva Questions

;