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BCECE Engineering BCECE Engineering Solved Paper-2014

  • question_answer
    The locus of a point \[P(\alpha ,\beta )\] moving under the condition that the line \[y=ax+\beta \] is a tangent to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], is

    A) a hyperbola                       

    B) a parabola

    C) a circle                 

    D) an ellipse     

    Correct Answer: A

    Solution :

    Given, line \[y=ax+\beta \]is a tangent to the given hyperbola, if\[{{\beta }^{2}}={{a}^{2}}{{\alpha }^{2}}-{{b}^{2}}\]. Hence, locus of \[(\alpha ,\beta )\] is\[{{y}^{2}}={{a}^{2}}{{x}^{2}}-{{b}^{2}}\]\[\Rightarrow \frac{{{y}^{2}}}{{{b}^{2}}}-\frac{{{x}^{2}}}{{{b}^{2}}/{{a}^{2}}}=1\]


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