If the point P denotes the complex number {\z}= {\x}+ {\iy} in the Argand plane and \frac{z-(2-i)}{z+(1+2 i)} is purely imaginary number, then the locus of P is [AP EAPCET 24 May 2025 S1]

Correct Answer is : a circle not containing the point (−1,−2) and having its centre on the line x+y+1=0

a hyperbola not containing the point (-1,-2)

an ellipse not containing the point (-1,-2)

a parabola not containing the point (-1,-2)

a circle not containing the point (-1,-2) and having its centre on the line x+y+1=0

AP EAPCET 24 May 2025 Shift 1 Paper

Section: Mathematics

Question : 7 of 160

Marks: +1, -0

If the point P denotes the complex number z=x+iy in the Argand plane and ‌

z−(2−i)

z+(1+2i)

is purely imaginary number, then the locus of P is

[AP EAPCET 24 May 2025 S1]

a hyperbola not containing the point (−1,−2)
an ellipse not containing the point (−1,−2)
a parabola not containing the point (−1,−2)
a circle not containing the point (−1,−2) and having its centre on the line x+y+1=0

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