Question

The locus of point `z` satisfying `R e(1/z)=k ,w h e r ek` is a nonzero real number, is a. a straight line b. a circle c. an ellipse d. a hyperbola
A. a stringht line
B. a circle
C. an ellispe
D. a hyperbola

Answer 1

Correct Answer - B
Let `z=x+iy`. Then,
`Re((1)/(z))=k`
`rArr Re((1)/(x+iy))=k`
`rArr Re((x)/(x^(2)+y^(2))-(iy)/(x^(2)+y^(2)))=k`
`rArr (x)/(x^(2)+y^(2))=k`
`rArr x^(2)+y^(2)-(1)/(k)x=0`
Which is a circle.