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Prove that |Z-Z1|^2+|Z-Z2|^2=a will repr...

Prove that `|Z-Z_1|^2+|Z-Z_2|^2=a` will represent a real circle [with center `(|Z_1+Z_2|^//2+)` ] on the Argand plane if `2ageq|Z_1-Z_1|^2`

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`|z-z_(1)|^(2)+|z-z_(2)|^(2)=a`
`implies(z-z_(1))(bar(z)-bar(z)_(1))+(z-z_(2))(bar(z)-bar(z)_(2))=a`
`implies2zbar(z)-z(bar(z)_(1)+bar(z)_(2))-bar(z)(z_(1)+z_(2))+z_(1)bar(z)_(1)+z_(2)bar(z)_(2)=a`
`implieszbar(z)=z((bar(z_(1))+bar(z_(2)))/(2))-bar(z)((z_(1)+z_(2))/(2))+(z_(1)bar(z)_(1)+z_(2)bar(z)_(2)-a)/(2)=0" "(1)`
Above equation is of the form `zbar(z)+alphabar(z)+bar(alpha)z+beta=0`, which represents the real circle if `alphabar(alpha)-betage0`
`implies((z_(1)+z_(2))(bar(z_(1))+bar(z_(2))))/(4)ge(z_(1)bar(z_(1))+z_(2)bar(z_(2))-a)/(2)`
`implies2agez_(1)bar(z_(1))+z_(2)bar(z_(2))-z_(1)bar(z_(2))-z_(2)bar(z_(1))`
`implies2age|z_(1)-z_(2)|^(2)`
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