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Show that the circle x^(2) + y^(2) + 4(x...

Show that the circle `x^(2) + y^(2) + 4(x+y) + 4 = 0` touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x+y+2 = 0 and which also passes through the origin.

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The correct Answer is:
`x^(2) + y^(2) + 2(x+y) = 0`
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