JEE Main & Advanced Mathematics Straight Line Question Bank Problems related to triangle and quadrilateral Locus

  • question_answer
    A point moves such that its distance from the point \[(4,\,0)\]is half that of its distance from the line \[x=16\]. The locus of this point is [AMU 1980]

    A)            \[3{{x}^{2}}+4{{y}^{2}}=192\]   

    B)            \[4{{x}^{2}}+3{{y}^{2}}=192\]

    C)            \[{{x}^{2}}+{{y}^{2}}=192\]       

    D)            None of these

    Correct Answer: A

    Solution :

               \[\sqrt{{{(h-4)}^{2}}+{{k}^{2}}}=\frac{1}{2}\left( \frac{h-16}{\sqrt{{{1}^{2}}+0}} \right)\]            Replace \[(h,k)\] by\[(x,\,y)\], we get \[3{{x}^{2}}+4{{y}^{2}}=192.\]


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