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If the foci of (x^(2))/(16)+(y^(2))/(4)=...

If the foci of `(x^(2))/(16)+(y^(2))/(4)=1` and `(x^(2))/(a^(2))-(y^(2))/(3)=1` coincide, the value of a is

A

3

B

2

C

`(1)/(sqrt(3))`

D

`sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
Foci of `(x^(2))/(16)+(y^(2))/(4) =1` are `(+- sqrt(12),0)`
Foci of `(x^(2))/(a^(2)) -(y^(2))/(3) =1` are `(+- sqrt(a^(2)+3), 0)`
Given `a^(2)+3 =12 rArr a^(2) = 9 rArr a = 3`
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