Home
Class 11
MATHS
If e is eccentricity of the ellipse (x^(...

If e is eccentricity of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`(where,a`lt`b), then

A

`b^(2)=a^(2)(1-e^(2))`

B

`a^(2)=b^(2)(1-e^(2))`

C

`a^(2)=b^(2)(e^(2)-1)`

D

`b^(2)=a^(2)(e^(2)-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that, `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1; altb`
We know that, `e=sqrt(1-(a^(2))/(b^(2)))rArre^(2)=((b^(2)-a^(2)))/(b^(2))`
`rArr b^(2)e^(2)=b^(2)=a^(2)`
`rArra^(2)=b^(2)(1-e^(2))`
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    NCERT EXEMPLAR|Exercise Fillers|6 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|16 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT EXEMPLAR|Exercise Fillers|16 Videos

Similar Questions

Explore conceptually related problems

If e is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 (a lt b ) , then ,

If e' is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 (a gt b) , then

Find the range of eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, (where a > b) such that the line segment joining the foci does not subtend a right angle at any point on the ellipse.

The eccentricity of the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) = 1 is always ,

If e_(1) is the eccentricity of the ellipse (x^(2))/(16)+(y^(2))/(b^(2))=1 and e_(2) is the eccentricity of the hyperbola (x^(2))/(9)-(y^(2))/(b^(2))=1 and e_(1)e_(2)=1 then b^(2) is equal to

A parabola is drawn whose focus is one of the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (where a>b) and whose directrix passes through the other focus and perpendicular to the major axes of the ellipse.Then the eccentricity of the ellipse for which the length of latus-rectum of the ellipse and the parabola are same is

Find the eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose latus rectum is half of its major axis.(a>b)