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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

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

B

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

C

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

D

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`.
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