The locus of the variable point $z=x+iy$ whose amplitude is always equal to $\theta$,is

  • A
    $x^2+y^2=\tan^2 \theta$
  • B
    $y=x \tan \theta$
  • C
    $\frac{x^2}{\sin^2 \theta}+\frac{y^2}{\cos^2 \theta}=1$
  • D
    $\frac{x^2}{\sin^2 \theta}-\frac{y^2}{\cos^2 \theta}=1$

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