Consider the following statements:
$I$. If $P(x_1, y_1)$ and $Q(x_2, y_2)$ are conjugate points with respect to the circle $x^2+y^2+2gx+2fy+c=0$,then $x_1x_2+y_1y_2+g(x_1+x_2)+f(y_1+y_2)+c=0$.
$II$. The pole of the line $x+y+1=0$ with respect to the circle $x^2+y^2=9$ is $(9, 9)$.
Which of the following is true?

• A
  Both $I$ and $II$ are true
• B
  Neither $I$ nor $II$ is true
• C
  $I$ is false and $II$ is true
• D
  $I$ is true and $II$ is false