1.

Point P represent the complex number z=x + iy and point Q represents the complex numberz+1/z. If P moves on thecircle |z| = 2, then the eccentricity of locus of point Q is

Answer»

`3//5`
`4//5`
`3//4`
`1//2`

Solution :Let `Q-=alpha+ibeta`
GIVEN that |z|=2, where z=x+iy
`:. x^(2)+y^(2)=4`
Now, `alpha+ibeta=z+(1)/(z)=(x+iy)+(1)/(x+iy)`
`=(x+iy)+((x-iy)/(4))=(5x)/(4)+(3iy)/(4)`
`:. alpha=(5x)/(4)and beta=(3y)/(4)`
Since `x^(2)+y^(2)=4`
`(16alpha^(2))/(25)+(16beta^(2))/(9)=4` ltbr So, LOCUS of point Q is `(x^(2))/(25)+(y^(2))/(9)=(1)/(4)`
Eccentricity of theis conic is given by
`e^(2)=1-(9)/(25)=(16)/(25)`


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