Yet another easy question

Algebra Level 5

Let $z$ be a complex number satisfying the relation

$~~~~~ z = 2 + t + i\sqrt{3 - t^2}.$

Find the locus of $z$ in argand plane. Where $t$ is a real parameter and $t^2\leq3$

Try more here

parabola circle Hyperbola Straight line Ellipse none of there

1 solution

Neelesh Vij
Feb 6, 2016

Good question post some more like this

Gauri shankar Mishra - 5 years, 4 months ago

Excellent problem! :)

Prakhar Bindal - 5 years, 3 months ago

Can u explain why is it not circle and how it's equation of semicircle

Dhruv Aggarwal - 5 years, 4 months ago

We know that the equation $y^2 + (x-2)^2 = (\sqrt{3})^2$ represents the equation of circle with center at $(2,0)$ and radius $\sqrt3$ . Now as the given condition is that $y = \sqrt{3 - t^2}$ so clearly $y>0$ so we have to the the part of circle which lies above x-axis ( i.e where $y>0$ ) Carefully observing, we see that the circle is symmetric about x-axis to the part that lies above the x-axis is a semicircle

neelesh vij - 5 years, 4 months ago

okay thnks Neelesh

Dhruv Aggarwal - 5 years, 4 months ago

Yet another easy question

1 solution

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