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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 12

  • question_answer
    The locus of the point of intersection of the lines \[\sqrt{3}x-y-4\sqrt{3}k=0\] and \[\sqrt{3}kx+ky-4\sqrt{3}=0\] for different value of A: is

    A) Circle                 

    B)   Parabola

    C) Hyperbola           

    D)   Ellipse

    Correct Answer: C

    Solution :

    Given, \[\sqrt{3}x-y=4\sqrt{3}k\]                        ...(i) \[k\left( \sqrt{3}x+y \right)=4\sqrt{3}\]                          ...(ii) Multiplying both \[e{{q}^{n}}\] (i) and (ii), get \[3{{x}^{2}}-{{y}^{2}}=48\] or \[\frac{{{x}^{2}}}{(48/3)}-\frac{{{y}^{2}}}{48}=1,\] which is a hyperbola.


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