Question

If z = x + iy and |z – 3| = R(z), then locus of z is-​

Answer 1

Answer:

Given |z – 2 + i| = |z – 3 – i|

z = x + iy

|x+iy – 2 + i| = |x+iy – 3 – i|

|(x-2)+(y+1)i| = |(x-3)+(y-1)i|

Taking modulus and squaring

(x-2)2+(y+1)2 = (x-3)2+(y-1)2

x2-4x+4+y2+2y+1 = x2-6x+9+y2-2y+1

-4x+2y+5+6x+2y-10 = 0

2x+4y-5 = 0