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Question

The equation of circle passing through the origin and point of intersection of circle x2+y2−2x+4y−20=0 and line x+y−1=0 is

A
x2+y2+22x16y=0
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B
x2+y2+22x+16y=0
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C
x2+y222x16y=0
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D
None of these
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Solution

The correct option is A x2+y222x16y=0
As the equation of circle passes through point of intersection of circles x2+y22x+4y20=0 and line x+y1=0
Let the equation of required circle is (x2+y22x+4y20)+λ(x+y1)=0
Since, it passes through origin.
Therefore, 20λ=0λ=20
Hence, the required equation of circle is
x2+y222x16y=0.

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