Let z=1−t+i√t2+t+2, where t is a real parameter. The locus of z in 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
a circle
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Solution
The correct option is A a hyperbola Given : z=1−t+i√t2+t+2
Let z=x+iy, then ⇒x=1−t,y=√t2+t+2
Eliminating t, y2=t2+t+2⇒y2=(1−x)2+1−x+2⇒y2=x2−3x+4⇒y2=(x−32)2+74∴y27/4−(x−32)27/4=1