A square is inscribed in the circle $x^{2} + y^{2} - 2 x + 4 y - 93 = 0$ with the sides parallel to the coordinate axes. The coordinate of the vertices are

(8, 5)

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(8, 9)

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(–6, 5)

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(–6, –9)

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Solution

The correct options are
A (8, 5)
C (–6, 5)
D (–6, –9)
Radius and center of the circle are (1, –2) and $7 \sqrt{2}$ respectively
Thus diameter of the circle is $14 \sqrt{2}$ and is equal to diagonal of the square, hence each side of square is 14. Since each side of the square are parallel to axes, let its equation be
x=a, x =b, y =c, y =d
also, r distance from center to each side of the circle

=7
This gives a = –6, b = 8, c =–9, d = 5
So vertices are (8, 5), (8, –9), (–6, 5), (–6, –9)

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