Question

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

• A. (8, 5)
• B. (8, 9)
• C. (-6, 5)
• D. (-6, -9)

Answer 1

Answer: (A), (C), (D)

The correct options are
A

(8, 5)

C

(-6, 5)

D

(-6, -9)

Radius and centre of the circle are (1,-2) and $7\sqrt{2}$ respectively. Thus, diameter of the circle is $14\sqrt{2}$ which is equal to diagonal of the square. So, each side of the square is $14$. Since each side of the square is parallel to axes, equation of all the lines forming the sides will be-

x = a, x = b, y = c, y = d

Also, r, the distance from center to each side of the square = 7

This gives a = -6, b = 8, c = -9, d = 5

So, vertices are (8,5),(8,-9),(-6,5),( -6,-9)