Complex Numbers And Quadratic Equations question 360
Question: If $ z=(\lambda +3)+i\sqrt{5-{{\lambda }^{2}},} $ then the locus of z is a
Options:
A) Circle
B) Straight line
C) Parabola
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ z=x+iy $ .Then $ x=\lambda +3 $ and $ y=\sqrt{5-{{\lambda }^{2}}} $
Þ $ {{(x-3)}^{2}}={{\lambda }^{2}} $ ……(i) and $ y^{2}=5-{{\lambda }^{2}} $ ……(ii) From (i) and (ii), $ {{(x-3)}^{2}}=5-y^{2} $
Þ $ {{(x-3)}^{2}}+y^{2}=5 $ . Obviously it is a circle.
BETA
