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

Geometry Level 4

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.

×