IIT JEE 1983 - 'Adapted' - Subjective to Multi-Correct Q6

The ends $A$ , $B$ of a straight line segment of constant length $c$ slide upon the fixed rectangular axes $OX$ , $OY$ , respectively. If the rectangular $OAPB$ is completed, then the locus of the foot of the perpendicular drawn from $P$ to $AB$ is $x^a+y^b=pc^q$ . Which of the following options is/are true?

• (A) $a+b>1$
• (B) $p=q$
• (C) $ap=\sqrt{bq}$
• (D) $\frac ab=p$

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 .