WBJEE · Maths · Parabola
For the real parameter \(t\), the locus of the complex number \(\mathrm{z}=\left(1-\mathrm{t}^2\right)+i \sqrt{1+\mathrm{t}^2}\) in the complex plane is
- A an ellipse
- B a parabola
- C a circle
- D a hyperbola
Answer & Solution
Correct Answer
(B) a parabola
Step-by-step Solution
Detailed explanation
Hints: Given \(\mathrm{z}=\left(1-\mathrm{t}^2\right)+\mathrm{i} \sqrt{1+\mathrm{t}^2}\) Let \(z=x+i y\) \(\begin{gathered} x=1-t^2 \\ y^2=1+t^2 \end{gathered}\) Thus, \(x+y^2=2\) \(\begin{aligned} & y^2=2-x \\ & y^2=-(x-2) \end{aligned}\) Thus parabola
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