Consider the following statements : I. If \(P\left(x_1, y_1\right)\) and \(Q\left(x_2, y_2\right)\) are conjugate points with respect to the circle \(x^2+y^2+2 g x+2 f y+c=0\), then \(x_1 x_2+y_1 y_2+g\left(x_1+x_2\right)+f\left(y_1+y_2\right)+c=0\) II. The pole of the line \(x+y+1=0\) with respect to the circle \(x^2+y^2=9\) is \((9,9)\). Then, which one of the following is true?

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.