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Question

The sides of a square are parallel to coordinate axes and it is inscribed in the circle x2+y22x+4y93=0. Find the coordinates of the vertices of the square.

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Solution

The given circle is (1,2) and 72. The sides are parallel to axes. Diagonal AC will be making an angle of 45o and BD will make an angle 135o with xaxis.
A and C will lie on x1cosθ=y+2sinθ=72C,72A
Put θ=45o C and A are (8,5) and (6,9)
B and D will lie on x1cosθ=y+2sinθ=72B,72D
Put θ=135o B and D are (6,5) and (8,9)

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