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Question

If the angle between the asymptotes of hyperbola x2a2y2b2=1 is π3. Then the eccentricity of conjugate hyperbola is

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Solution

We know that, angle between asymptotes of hyperbola is 2tan1(ba)
2tan1(ba)=π3
ba=tan(π6)
ba=13
Now,
eccentricity, e=1+b2a2
e=1+13=43
Let e be the eccentricity of conjugate ​hyperbola
1e2+1e2=1
1e2+34=1
1e2=14
​​​​​e=2

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