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The equation of the circle which passes ...

The equation of the circle which passes through the origin, center lies on the line x+y = 4 and cuts the circle `x^2 + y^2 - 4x + 2y +4 = 0` orthogonally :

Text Solution

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Center on X+Y=4
Distance from origin=r
`sqrt(h^2+(4-h)^2)=r`
`C_2:x^2+y^2-4x+2y+4=0`
`x^2-2*2x+y^2+2y+4-4+1-4+4=0`
`(x-1)^2+(y+1)^2-4-1+4=0`
`(x-1)^2+(y+1)^2=1`
`C=(1,-1),r=1`
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