Home
Class 12
MATHS
If the eccentricity of the ellipse,x^2/(...

If the eccentricity of the ellipse,`x^2/(a^2+1)+y^2/(a^2+2)=1` is `1/sqrt6` then latus rectum of ellipse is

A

`5//sqrt(6)`

B

`10//sqrt(6)`

C

`8//sqrt(6)`

D

none of these

Text Solution

Verified by Experts

Here , `a^(2)+2gta^(2)+1`
`:. a^(2)+1=(a^(2)+2)(1-e^(2))`
` or a^(2)+1=(a^(2)+2)(5)/(6)`
`or 6a^(2)+6=a^(2)+10`
`or a^(2)=10-6=4`
Latus reactum `=(2(a^(2)+1))/(sqrt(a^(2)+2))=(2xx5)/(sqrt(6))=(10)/(sqrt(6))`
Promotional Banner

Similar Questions

Explore conceptually related problems

The eccentricity of the ellipse 5x^(2) + 9y^(2) = 1 is _

The eccentricity of the ellipse 25 x^(2) + 4y^(2) = 100 is _

The eccentricity of the ellipse 4x^(2) + 25y^(2) = 100 is _

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

Calculate the eccentricity of the ellipse (x^(2))/(169)+(y^(2))/(144) = 1

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

What is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 if length of its minor axis is equal to the distance between its foci ?

Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 be reciprocal to that of the ellipse x^(2)+4y^(2)=4 . If the hyperbola passes through a focus of the ellipse, then

Find the equation of the normal to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the positive end of the latus rectum.