AP EAMCET · Maths · Complex Number
If the point P denotes the complex number \(\mathrm{z}=\mathrm{x}+\mathrm{iy}\) in the Argand plane and \(\frac{z-(2-i)}{z+(1+2 i)}\) is purely imaginary number, then the locus of \(P\) is
- A a hyperbola not containing the point \((-1,-2)\)
- B an ellipse not containing the point \((-1,-2)\)
- C a parabola not containing the point \((-1,-2)\)
- D a circle not containing the point \((-1,-2)\) and having its centre on the line \(x+y+1=0\)
Answer & Solution
Correct Answer
(D) a circle not containing the point \((-1,-2)\) and having its centre on the line \(x+y+1=0\)
Step-by-step Solution
Detailed explanation
The locus of \\(z\\) for which \\(\frac{z-z_1}{z-z_2}\\) is purely imaginary is a circle with \\(z_1\\) and \\(z_2\\) as the endpoints of a diameter. Here, \\(z_1 = 2-i\\) (point \\(A(2,-1)\\)) and \\(z_2 = -(1+2i)\\) (point \\(B(-1,-2)\\)). Equation of the circle with diameter…
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