Home
Class 12
MATHS
The equation to the hyperbola having its...

The equation to the hyperbola having its eccentricity 2 and the distance between its foci is 8 is

A

`(x^(2))/(12)-(y^(2))/(4)=1`

B

`(x^(2))/(4)-(y^(2))/(12)=1`

C

`(x^(2))/(8)-(y^(2))/(2)=1`

D

`(x^(2))/(16)-(y^(2))/(9)=1`

Text Solution

Verified by Experts

The correct Answer is:
B
Distance between foci = 8
`:. 2ae = 8` also `e = 2, :. 2a = 4`
`rArr a = 2 rArr a^(2) = 4 :. b^(2) = 4(4-1) = 12`
`:.` Equation of hyperbola is `(x^(2))/(4) -(y^(2))/(12) =1`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the equation of the hyperbola with eccentricity sqrt(2) and the distance between whose foci is 16.

Find the equation of the hyperbola whose eccentricity is sqrt(2) and the distance between the foci is 16, taking transverse and conjugate axes of the hyperbola as x and y-axes respectively.

Find th equation of the hyperbola eccentricity is 2 and the distance between foci 16.

Write the equation of the hyperbola of eccentricity sqrt(2) if it is known that the distance between its foci is 16.

Find the equation of the hyperbola in standard form , if : eccentricity = 3/2 and distance between directrices = 8/3

if in a hyperbola the eccentricity is sqrt(3) and the distance between the foci is 9 then the equation of hyperbola in the standard form is:

Equation of the hyperbola with eccentricity (3)/(2) and foci at (2,0) is