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

  • question_answer
    O is the origin and A is the point (3, 4). If a point P moves so that the line segment OP is always parallel to the line segment OA, then the equation to the locus of P is  

    A) \[4x-3y=0\]

    B) \[4x+3y=0\]

    C) \[3x+4y=0\]

    D) \[3x-4y=0\]

    Correct Answer: A

    Solution :

    Since OA and OP will be parallel only when O, A and P are collinear. Therefore, \[\left| \,\begin{matrix}    0 & 0 & 1  \\    3 & 4 & 1  \\    x & y & 1  \\ \end{matrix}\, \right|=0\,\,\Rightarrow \,\,4x-3y=0\].


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