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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 |
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Answer» `3//5` 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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