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JCECE Engineering JCECE Engineering Solved Paper-2009

  • question_answer
    Equation of the tangent to the hyperbola\[2{{x}^{2}}-3{{y}^{2}}=6\]. Which is parallel to the line \[y-3x-4=0\]is

    A) \[y=3x+8\]                         

    B) \[y=3x-8\]

    C) \[y=3x+2\]                         

    D)  None of these

    Correct Answer: D

    Solution :

    Let the equation of a line which is parallel to the line\[y-3x-4=0\]is                 \[y=3x+k\] Since, this is tangent to the hyperbola                 \[\frac{{{x}^{2}}}{3}-\frac{{{y}^{2}}}{2}=1\] \[\therefore \]       \[k=\sqrt{3{{(3)}^{2}}-2}\]      \[(\because \,\,k=\sqrt{{{a}^{2}}{{m}^{2}}-{{b}^{2}}})\]                 \[=\sqrt{25}=5\] \[\therefore \]Required line is\[y=3x+5\],


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