Through a random point \((p,q)\) on the Cartesian plane, secants are drawn to the circle \(x^2+y^2=r^2\). If the locus of mid-points of the secants to the circle is \(x^2+2hxy+y^2+2gx+2fy+c=0\), then which of the following options are definitely true?

- (A) \(h=pq\)
- (B) \(g=p\)
- (C) \(f=q\)
- (D) \(c=0\)

Enter your answer as a 4 digit string of 1s and 9s, using 1 for correct option, 9 for wrong. For example, 1199 indicates A and B are correct, C and D are incorrect. None, one or all may also be correct.

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