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Question

Let z=1t+it2+t+2, where t is a real parameter. The locus of z in the argand plane is:

A
a hyperbola
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B
an ellipse
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C
a straight line
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D
None of these
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Solution

The correct option is A a hyperbola
Let z=x+iy, then

x+iy=1t+it2+t+2x=1t,y=t2+t+2

Putting t=1x in the other relation, we get

y2=t2+t+2=(1x)2+1x+2=(x32)2+74

y2(x34)2=74, which is a hyperbola.

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