A square is inscribed in the circle x2+y2−2x+4y−93=0 with its sides parallel to the coordinate axes. The coordinates of its vertices are
(-6, -9), (-6, 5), (8, -9) and (8, 5)
Let x = a, x = b, y = c and y = d be the sides of the square. The length of each diagonal of the square is equal
to the diameter of the circle i.e., 2√1+4+93. Let l be the length of each side of the square.
Then 2l2=(Diagonal)2⇒2l2=(2.√1+4+93)2 ⇒ l = 14
Therefore each side of the square is at a distance 7 from the centre (1, -2) of the given circle. This implies
that a = -6, b = 8, c = -9, d = 5.
Therefore the vertices of the square are (-6, -9), (-6, 5), (8, -9), (8, 5).