AP EAMCET · Maths · Complex Number
The locus of \(z\) satisfying \(\left|\frac{z-i}{z-2 i}\right|=2\) is a
- A Hyperbola
- B Circle
- C Straight line
- D Ellipse
Answer & Solution
Correct Answer
(B) Circle
Step-by-step Solution
Detailed explanation
It is given that, \(\left|\frac{z-i}{z-2 i}\right|=2\) Let \(z=x+i y\), then \(\begin{aligned} & |x+i(y-1)|=2|x+(y-2) i| \\ \Rightarrow \quad & x^2+(y-1)^2=4\left[x^2+(y-2)^2\right] \\ \Rightarrow & 3 x^2+3 y^2-14 y+16=0 \text { represent a circle, so } \end{aligned}\) locus of…
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