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JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    The eccentricity of the hyperbola \[5{{x}^{2}}-4{{y}^{2}}+20x+8y=4\] is              [UPSEAT 2004]

    A)            \[\sqrt{2}\]                               

    B)            \[\frac{3}{2}\]

    C)            2     

    D)            3

    Correct Answer: B

    Solution :

               Given equation of hyperbola is \[5{{x}^{2}}-4{{y}^{2}}+20x+8y=4\] \[5{{(x+2)}^{2}}-4\,{{(y-1)}^{2}}=20\] Þ \[\frac{{{(x+2)}^{2}}}{4}-\frac{{{(y-1)}^{2}}}{5}=1\] From\[{{b}^{2}}={{a}^{2}}({{e}^{2}}-1)\],\[5=4({{e}^{2}}-1)\] \[\Rightarrow {{e}^{2}}=9/4\Rightarrow e=3/2\].


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