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JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    Locus of the point of intersection of straight lines \[\frac{x}{a}-\frac{y}{b}=m\] and \[\frac{x}{a}+\frac{y}{b}=\frac{1}{m}\] is      [MP PET 1991, 2003]

    A)            An ellipse                                  

    B)            A circle

    C)            A hyperbola                               

    D)            A parabola

    Correct Answer: C

    Solution :

                       \[\frac{x}{a}-\frac{y}{b}=m\]                                                   .....(i)                     \[\frac{x}{a}+\frac{y}{b}=\frac{1}{m}\]                                                               .....(ii)                    Multiplying equation (i) and (ii),                    \[\left( \frac{x}{a}-\frac{y}{b} \right)\,\left( \frac{x}{a}+\frac{y}{b} \right)=m.\frac{1}{m}\]                    \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], which is the equation of hyperbola.


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