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Let f(z) is of the form alpha z +beta , wherealpha, beta,z are complex numbers such that |alpha| ne |beta|.f(z) satisfies followingproperties : (i)If imaginary part of z is non zero, then f(z)+bar(f(z)) = f(barz)+bar(f(z)) (ii)If real part of of z is zero , then f(z)+bar(f(z)) =0 (iii)If z is real , then bar(f(z)) f(z) gt (z+1)^2 AA z in R (4x^2)/((f(1)-f(-1))^2)+y^2/((f(0))^2)=1 , x , y in R, in (x,y) plane will represent :

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HYPERBOLA
CIRCLE
ellipse
pair of line

Answer :A


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