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JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank Geometry of complex numbers

  • question_answer
    If  \[arg\,(z-a)=\frac{\pi }{4}\], where \[a\in R\],  then the locus of \[z\in C\] is a [MP PET 1997]

    A) Hyperbola

    B) Parabola

    C) Ellipse

    D) Straight line

    Correct Answer: D

    Solution :

    \[arg\left\{ (x-a)+iy \right\}=\frac{\pi }{4}\]Þ\[{{\tan }^{-1}}\left( \frac{y}{x-a} \right)=\frac{\pi }{4}\] Þ \[\frac{y}{x-a}=\tan \frac{\pi }{4}=1\,\,\,\Rightarrow \]\[x-a=y\]


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