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
  $\frac{x^2}{\sin^2 \theta}-\frac{y^2}{\cos^2 \theta}=1$