Considr ΔABC in argand plane.Let A(0),B(1),C(1+i) be its vertices and M be mid point of CA.Let z be variable complex number in the plane.Let u be another variable complex number u=z2+1
Q1Find locus of u when z is on BM
Q2FInd axis of locus of u when z is on BM
Q3Whatis directrix of locus of u when z is on BM
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1 Answers
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Converting the entire thing into Co-ordinate Geometry, we have eqn of BM as x+y=1.
Meaning z is of the form h+i(1-h)
So If (x,y) be the point of u at some instant we have
x=h^2-(1-h)^2\\ \ y=2h(1-h)
h=\frac{x+1}{2}
Putting it in the 2nd eqn we have locus as
\boxed{ 2y=1-x^2} - which is that of a parabola.
