Home
Class 12
MATHS
Point P represent the complex number z=x...

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

A

`3//5`

B

`4//5`

C

`3//4`

D

`1//2`

Text Solution

Verified by Experts

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)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Amplitude of the complex number z= 1 is

Represent the complex number z=1+isqrt(3) in the polar form.

The amplitue of the complex number z = - 2 is

A point P which represents a complex number z, moves such that |z-z_(1)|= |z-z_(2)|, then the locus of P is-

If |z-1-i|=1 , then the locus of a point represented by the complex number 5(z-i)-6 is

Find the complex number z=e^(i(pi)) in the form x+iy .

Find the locus of the points representing the complex number z for which |z+5|^2-|z-5|^2=10.

If z ne 1 and (z^2)/(z-1) is real then the point represented by the complex number z lies

The points representing the complex number z for which arg((z-2)/(z+2))=pi/3 lie on

The points representing the complex number z for which arg ((z-2)/(z+2))=(pi)/(3) lie on -