The locus of point `z` satisfying `R e(1/z)=k , where k` is a non zero real number, is a. a straight line b. a circle c. an ellipse d. a hyperbola

Options

A. a stringht line
B. a circle
C. an ellispe
D. a hyperbola

Answer

B

Explanation

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.