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If z(1) and z(2) are two fixed points in...

If `z_(1) and z_(2)` are two fixed points in the Argand plane, then find the locus of a point z in each of the following
`|z-z_(1)|= k|z-z_(2)|, k in R^(+), k ne 1`

A

a circle

B

a parabola

C

an ellipse

D

a hyperbola

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`|z-z_(1)|=k|z-z_(2)|`
`rArr` PA=kPB
`rArr (PA)/(PB) = k rArr` Locus of P is a cycle.
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OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Chapter Test
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  11. The condition that x^(n+1)-x^(n)+1 shall be divisible by x^(2)-x+1 is ...

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  12. The expression (1+i)^(n1)+(1+i^(3))^(n2) is real iff

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  13. If |{:(6i,3i,1),(4,3i,-1),(20,3,i):}|=x+iy, then (x, y) is equal to

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  18. If 2z1-3z2 + z3=0, then z1, z2 and z3 are represented by

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  19. If Re((z+4)/(2z-1)) = 1/2 then z is represented by a point lying on

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  20. The vertices of a square are z(1),z(2),z(3) and z(4) taken in the anti...

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  21. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

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