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  • Need explanation for: A hyperbola has its centre at the origin, passes through the point (4,2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is :

 

A hyperbola has its centre at the origin, passes through the point (4,2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is :

  • Option 1)

     

    2

  • Option 2)

     

    \sqrt{3}

  • Option 3)

     

    2/\sqrt{3}

  • Option 4)

     

    3/2

Answers (1)

best_answer

 

Eccentricities of Hyperbola -

\frac{1}{e_{1}^{2}}+\frac{1}{e_{2}^{2}}= 1

- wherein

e_{1}\, and \, e_{2}  are eccentricities of the hyperbola and its conjugate.

 

 

Hyperbola -

Hyperbola is locus of all the points in a plane ,the difference of whose distance from two fixed point is constant.

- wherein

 

Standard equation of hyperbola is 

\frac{x^2}{a^2} - \frac{y^2}{b^2} =1

2a = 4 \Rightarrow a =2

so,

\frac{x^2}{4} - \frac{y^2}{b^2} =1 passes through (4,2)

\\4 - \frac{4}{b^2} = 1\\ b^2 = \frac{4}{3}

eccentricity of hyperbola : e = \sqrt{1 + \frac{b^2}{a^2}}

e = \frac{2}{\sqrt3}

 


Option 1)

 

2

Option 2)

 

\sqrt{3}

Option 3)

 

2/\sqrt{3}

Option 4)

 

3/2

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