TS EAMCET · Maths · Complex Number
If \(z=x+i y\) and if the point P represents \(z\) in the Argand plane, then the locus of \(z\) satisfying the equation \(|z-1|+|z+i|=2\) is
- A \(15 x^2-2 x y+15 y^2-16 x+16 y-48=0\)
- B \(3 x^2+2 x y+3 y^2-4 x-4 y=0\)
- C \(3 x^2-2 x y+3 y^2-4 x+4 y=0\)
- D \(15 x^2+2 x y+15 y^2+16 x-16 y-48=0\)
Answer & Solution
Correct Answer
(C) \(3 x^2-2 x y+3 y^2-4 x+4 y=0\)
Step-by-step Solution
Detailed explanation
\(z=x+i y\)...(i) \(\begin{aligned} & |z-1|+|z+i|=2 \\ & |(x-1)+i y|+|x+i(1+y)|=2 \\ & \Rightarrow \sqrt{(x-1)^2+y^2}+\sqrt{x^2+(y+1)^2}=2 \\ & \Rightarrow \sqrt{(x-1)^2+y^2}=2-\sqrt{x^2+(y+1)^2} \end{aligned}\) (from (i)) Squaring both sides,…
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