TS EAMCET · Maths · Complex Number
If \(z_1=2-3 i\) and \(z_2=-1+i\), then the locus of a point \(P\) represented by \(z=x+i y\) in the argand plane satisfying the equation \(\arg \left(\frac{z-z_1}{z-z_2}\right)=\frac{\pi}{2}\) is
- A \(x^2+y^2-x+2 y-5=0\)
- B \(x^2+y^2-x+2 y-5=0\) and \(4 x+3 y+1 < 0\)
- C \(4 x+3 y+1=0\) and \(x^2+y^2-x+2 y-5>0\)
- D \(x^2+y^2-x+2 y-5=0\) and \(4 x+3 y+1>0\)
Answer & Solution
Correct Answer
(D) \(x^2+y^2-x+2 y-5=0\) and \(4 x+3 y+1>0\)
Step-by-step Solution
Detailed explanation
We have, \( \begin{aligned} & z_1=2-3 i, z_2=-1+i \\ & \text { and } \arg \left(\frac{z-z_1}{z-z_2}\right)=\frac{\pi}{2} \end{aligned} \) \(\therefore\left|z-z_1\right|^2+\left|z_2-z_2\right|^2=\left|z_1-z_2\right|^2\)…
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