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Question

A square is inscribed in the circle x2+y22x+4y+3=0, whose sides are parallel to the coordinate axes. One vertex of the square is

A
(1+2,2)
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B
(12,2)
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C
(1,2+2)
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D
None of these
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Solution

The correct option is D None of these
REF.Image.
Given equation of circle is X2+y22x+4y+3=0
(x1)2+(y+2)2=2
So, 0=Center=(1,2)
radius =2
So, AO=OC=2
Let the length of the side be a.
then length of diagnal = 2r
2a=2×2
a=2
slope is AC is 45 (assuming it to be lie 1 to x-axis)
So, coordinates of A, C are
(1±2cos45,2±2sin45)
= (2, -1) and (0, -3)
A=(0,3)B=(0+2,3)=(2,3)
C=(0,3+2)=(0,1)
Vectors are (0,-3), *(2,-3), (2,-1), (0,-1).$

1155187_1110670_ans_6fc704b712e448e481651496eff0c8b8.jpg

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