A straight line through the fixed point $(2, 3)$ intersects the coordinate axes at distinct points $P$ and $Q$. If $O$ is the origin and the rectangle $OPRQ$ is completed (so $R$ is the fourth vertex), the locus of $R$ is:
Step-by-Step Solution
Key Concept: Let $P = (a, 0)$ and $Q = (0, b)$. The line $PQ: x/a + y/b = 1$ passes through $(2, 3)$, giving $2/a + 3/b = 1$. The fourth vertex $R = (a, b)$ satisfies this same relation with $x = a, y = b$.
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Correct Answer: (2)