JEE Main & Advanced Mathematics Rectangular Cartesian Coordinates Question Bank Transformation of axes and Locus

  • question_answer
    A point P moves so that its distance from the point \[(a,0)\]is always equal to its distance from the line \[x+a=0\]. The locus of the point is [MP PET 1982]

    A) \[{{y}^{2}}=4ax\]

    B) \[{{x}^{2}}=4ay\]

    C) \[{{y}^{2}}+4ax=0\]

    D) \[{{x}^{2}}+4ay=0\]

    Correct Answer: A

    Solution :

    \[{{(x-a)}^{2}}+{{y}^{2}}={{(x+a)}^{2}}\,\,\Rightarrow \,\,{{y}^{2}}=4ax\] Note: This is also the definition of parabola\[{{y}^{2}}=4ax.\]


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