Complex Numbers And Quadratic Equations question 467
Question: Let $ z=1-t+i \sqrt{t^{2}+t+2} $ , where t is a real parameter. The locus of z in the argand plane is
Options:
A) a hyperbola
B) an ellipse
C) a straight line
D) none of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ x+iy=1-t+i\sqrt{t^{2}+t+2} $
$ \Rightarrow x=1-t,y=\sqrt{t^{2}+t+2} $ Eliminating t, $ y^{2}=t^{2}+t+2={{(1-x)}^{2}}+1-x+2={{( x-\frac{3}{2} )}^{2}}+\frac{7}{4} $
$ \Rightarrow y^{2}-{{( x-\frac{3}{2} )}^{2}}=\frac{7}{4} $ , which is a hyperbola
BETA
