Home
Class 12
MATHS
A focus of an ellipse is at the origi...

A 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 the semimajor axis is (1) `8/3` (2) `2/3` (3) `4/3` (4) `5/3`

Text Solution

AI Generated Solution

To solve the problem step by step, we will use the properties of an ellipse related to its focus, directrix, and eccentricity. ### Step 1: Understand the given information We have: - Focus of the ellipse at the origin (0, 0). - Directrix is the line \( x = 4 \). - Eccentricity \( e = \frac{1}{2} \). ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    JEE MAINS PREVIOUS YEAR ENGLISH|Exercise All Questions|10 Videos

  • HYPERBOLA

    JEE MAINS PREVIOUS YEAR ENGLISH|Exercise All Questions|2 Videos

Similar Questions

Explore conceptually related problems

A 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 the semi-major axis is

Find equation of the ellipse whose focus is (1,-1), then directrix the line x-y-3=0 and eccentricity 1/2 is

Find the equation of Hyperbola with one focus at the origin and directrix x+3=0 and eccentricity sqrt3

An ellipse has directrix x+y=-2 focus at (3,4) eccentricity =1/2, then length of latus rectum is

The equation of the hyperbola whose focus is (1,2) , directrix is the line x+y+1=0 and eccentricity 3//2 , is

The focus and the correspondin directrix of a hyperbola are (1-3) and y=2 and eccentricity is 3/2. Find the equation of the hyperbola.

Let the distance between a focus and the corresponding directrix of an ellipse be 8 and the eccentricity be 1/2 . If the length of the minor axis is k , then (sqrt(3)k)/2 is ____________

Let the distance between a focus and the corresponding directrix of an ellipse be 8 and the eccentricity be 1/2 . If the length of the minor axis is k , then (sqrt(3)k)/2 is ____________

Find the equation to the ellipse whose one focus is (2, 1), the directrix is 2x-y+3=0 and the eccentricity is 1/sqrt(2)

Find the equation to the ellipse whose one focus is (2, 1) , the directrix is 2x-y+3=0 and the eccentricity is 1/sqrt(2) .

Home
Profile