January 11th, 2017, 04:19 AM  #1 
Newbie Joined: Jan 2017 From: Pakistan Posts: 1 Thanks: 0  locus of z=at+b/t
Please find locus of z=at+b/t where a and b are complex constants and t is real. I started with a= a1+a2i and b=b1+b2i but stuck at x=a1t+b1/t, y=a2+b2/t how to eliminate t? so that I can get equation in terms of x and y only? Thanks in advance. 
January 11th, 2017, 07:39 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,059 Thanks: 1618 
If x = at + b/t and y = ct + d/t, dx  by = (ad  bc)t and cx + ay = (ad  bc)/t. The product of those equations eliminates t. 

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