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If a circle Passes through point (1,2) a...

If a circle Passes through point (1,2) and orthogonally cuts the circle `x^2 + y^2 = 4`, Then the locus of the center is:

Text Solution

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`(C_1P)^2+(C_2P)^2=(C_1C_2)^2`
`h^2+k^2=4+r^2-(1)`
`(h-1)^2+(k-2)^2=r^2`
subtracting equation 2 from 1
`h^2+k^2-(h-1)^2-(k-1)^2=4+r^2-r^2`
`h^2+k^2-h^2+2h-1-k^2+4k-4=4`
2h+4=9
2x+4y=9.
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