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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The equation of the locus of a point which moves so as to be at equal distances from the point (a, 0) and the y-axis is

    A)            \[{{y}^{2}}-2ax+{{a}^{2}}=0\]   

    B)            \[{{y}^{2}}+2ax+{{a}^{2}}=0\]

    C)            \[{{x}^{2}}-2ay+{{a}^{2}}=0\]   

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

    Correct Answer: A

    Solution :

               Accordingly,\[{{(h-a)}^{2}}+{{k}^{2}}={{h}^{2}}\]                    Þ \[-2ah+{{a}^{2}}+{{k}^{2}}=0\]                    Replace (h, k) by (x, y), then \[{{y}^{2}}-2ax+{{a}^{2}}=0\] is the required locus.


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