IIT JEE 1983 - 'Adapted' - Subjective to Multi-Correct Q4

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.

In case you are preparing for IIT JEE, you may want to try IIT JEE 1983 Mathematics Archives .