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Question

The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines
x2y22x+4y3=0, is


A

x2+y22x4y+4=0

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B

x2+y2+2x+4y4=0

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C

x2+y22x+4y+4=0

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D

None of these

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Solution

The correct option is A

x2+y22x4y+4=0


Let the required equation of the circle be (xh)2+(yk)2=a2

Comparing the given equation x22x+4y3=0
with ax2+by2+2hxy+2gx+2fy+c=0
we get :

a=1,b1,h=0,g=1,f=2,c=3

Intersection point

=(hfbgabh2,ghafabh2)=(11,21)=(1,2)

Thus, the centre of the circle is (1, 2).

The equation of the required circle is

(x1)2+(y2)2=a2

Since circle passes through (1, 1), we have
1=a2

Equation of the required circle :

(x1)2+(y2)2=1

x2+y22x4y+4=0


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