A square is inscribed in the circle $x^2 + y^2 - 2x + 4y - 93 = 0$ with the sides parallel to the coordinate axes. The coordinates of the vertices are:
Step-by-Step Solution
Key Concept: For a square inscribed in a circle with sides parallel to axes, the diagonals have slopes $\pm 1$ and bisect each other at the circle's center.
Since sides of the square are parallel to coordinate axes, slopes of $PR$ and $SQ$ are $1$ and $-1$ respectively. Using the constraint that vertices lie on circle $x^2 + y^2 = 18$ and the slope conditions, the coordinates of $P$ and $Q$ are found to be $(8,5)$ and $(-6,-9)$. Similarly, $S$ and $R$ have coordinates $(-6,5)$ and $(8,-9)$.
Correct Answer: 1,3,4