Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20206 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Ellipse

JEE Main 2020 · 6 September · Evening Shift · Mathematics · Ellipse

If the normal at an end of latus rectum of an ellipse passes...

If the normal at an end of latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity ee of the ellipse satisfies :

Options

  1. Ae4+2e2−1=0{e}^{4} + 2{e}^{2} - 1 = 0
  2. Be2+e−1=0{e}^{2} + e - 1 = 0
  3. Ce4+e2−1=0{e}^{4} + {e}^{2} - 1 = 0
  4. De2+2e−1=0{e}^{2} + 2e - 1 = 0

Correct answer

C. e4+e2−1=0{e}^{4} + {e}^{2} - 1 = 0

Step-by-step solution

Equation of normal at (ae,b2a)\left(ae, \dfrac{{b}^{2}}{a}\right)

a2xae−b2yb2/a=a2−b2\dfrac{{a}^{2}x}{ae} - \dfrac{{b}^{2}y}{{b}^{2} / a} = {a}^{2} - {b}^{2}

it passes through (0,−b)( 0, - b )

ab=a2e2ab = {a}^{2}{e}^{2}

a2b2=a4e4(∵b2=a2(1−e2)</p><p>{a}^{2}{b}^{2} = {a}^{4}{e}^{4}\left(∵ {b}^{2} = {a}^{2} ( 1 - {e}^{2}\right)</p><p>1 - {e}^{2} = {e}^{4}</p></p>

Practice Ellipse on Quantrex Academy →

More from Ellipse

Consider the ellipse E given by (x^2)/(18) + (y^2)/(12) = 1 . Let H be the hyperbola… JEE Advanced 2026Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: Let… JEE Advanced 2026Let (x^2)/(f(a^2+7a+3)) + (y^2)/(f(3a+15)) = 1 represent an ellipse with major axis along… JEE Main 2026The eccentricity of an ellipse E with centre at the origin O is 3 2 and its directrices… JEE Main 2026Let x = 9 be a directrix of an ellipse E , whose centre is at the origin and eccentricity… JEE Main 2026Let a focus of the ellipse E: (x^2)/(a^2) + (y^2)/(b^2) = 1 be S(4, 0) and its… JEE Main 2026Let A be the point (3, 0) and circles with variable diameter AB touch the circle x^2 +… JEE Main 2026Let an ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1 , a < b , pass through the point (4, 3) and… JEE Main 2026An ellipse has its center at (1,-2) , one focus at (3,-2) and one vertex at (5,-2) . Then… JEE Main 2026Let the ellipse E: x^ 2 144 + y^ 2 169 =1 and the hyperbola H: x^ 2 16 - y^ 2 λ^ 2 =-1… JEE Main 2026Let the length of the latus rectum of an ellipse x^ 2 a^ 2 + y^ 2 b^ 2 =1,(a>b) , be 30.… JEE Main 2026Let (h, k) lie on the circle C: x^ 2 +y^ 2 =4 and the point (2 h+1,3 k+2) lie on an… JEE Main 2026Let each of the two ellipses E_ 1 : x^ 2 a^ 2 + y^ 2 b^ 2 =1,(a>b) and E_ 2 : x^ 2 ~A^ 2… JEE Main 2026Let the line y-x=1 intersect the ellipse x^ 2 2 + y^ 2 1 =1 at the points A and B. Then… JEE Main 2026Let S and S^ be the foci of the ellipse x^ 2 25 + y^ 2 9 =1 and P(α, β) be a point on the… JEE Main 2026If the line α x+4 y= 7 , where α ∈ R , touches the ellipse 3 x^ 2 +4 y^ 2 =1 at the point… JEE Main 2026 Full Ellipse list Ellipse JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs