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Question: A square is inscribed in the circle \(x ^ { 2 } + y ^ { 2 } - 2 x + 4 y + 3 = 0\), whose sides are p...

A square is inscribed in the circle x2+y2−2x+4y+3=0x ^ { 2 } + y ^ { 2 } - 2 x + 4 y + 3 = 0, whose sides are parallel to the coordinate axes. One vertex of the square is.

A

(1+2,−2)( 1 + \sqrt { 2 } , - 2 )

B

(1−2,−2)( 1 - \sqrt { 2 } , - 2 )

C

(1,−2+2)( 1 , - 2 + \sqrt { 2 } )

D

None of these

Answer

None of these

Explanation

Solution

Trick : Obviously the centre of the given circle is (1,−2)( 1 , - 2 ). Since the sides of square are parallel to the axes, therefore, first three alternates cannot be vertices of square because in first two (a and b) y=−2y = - 2 and in (3)x=1x = 1, which passes through centre (1,−2)( 1 , - 2 ) but it is not possible. Hence answer (4) is correct.