Question:medium

If \( z = x+iy \) and the point \( P \) denotes \( z \) in the Argand plane, then the locus of \( P \) satisfying the condition \( \text{Im}\left(\frac{z-3i}{z+2}\right) = 1, z \neq -2 \) is:

Show Hint

For \( \text{Im}\left(\frac{z-z_1}{z-z_2}\right) = k \), if \( k \neq 0 \), the locus is always a circle. If \( k=0 \), the locus is a straight line. Here, \( k=1 \), so look for the equation representing a circle.
Updated On: Jul 18, 2026
  • \( 7x - 2y + 10 = 0 \)
  • \( x^2 + xy + y^2 + 7x - 2y + 10 = 0 \)
  • \( x^2 - xy + y^2 + 7x - 2y + 10 = 0 \)
  • \( x^2 + y^2 + 7x - 2y + 10 = 0 \)
Show Solution

The Correct Option is D

Solution and Explanation

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