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KVPY Sample Paper KVPY Stream-SX Model Paper-7

  • question_answer
    The equation of a tangent to the hyperbola \[4{{x}^{2}}-5{{y}^{2}}=20\]  parallel to the line \[x-2y=2\]is:

    A) \[x-y+1=0\]                  

    B)  \[x-y+7=0\]

    C) \[x-y+9=20\]    

    D) \[x-y-3=0\]

    Correct Answer: A

    Solution :

    Hyperbola is \[\frac{{{x}^{2}}}{5}-\frac{{{y}^{2}}}{4}=1\]
    Equation of its tangent in slope from is \[y=mx\pm \sqrt{5{{m}^{2}}-4}\]
    Hence, tangent with slope 1 is \[y=x\pm 1.\]


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