find the eccentricity of the hyperbola if the transverse axis and the conjugate axis are the same length.

Question

HELP! Can someone help me here How to answer this

Answer 1

Hi Pedro, the general formula for a hyperbola is:

 

x² / a² - y² / b² = 1

 

The eccentricity of the hyperbola is given by: e = √(a² +b²)  / a

 

If the transverse axis and the conjugate axis are the same length, that means a and b are equal.

 

The eccentricity becomes: e = √(a² + a²) / a.

 

e = √(2a²) / a

 

e = a * √2 / a

 

e = √2

 

The eccentricity of a hyperbola when the transverse axis and the conjugate axis are the same length is: e = √2.

 

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