1. Tardigrade
  2. Question
  3. Mathematics
  4. Let z be a complex number Assertion (A) :The equation |z - 1| - |z - i| = 1 represents a hyperbola. Reason (R): The equation |z - z1| - |z - z2| = k is a hyperbola.

Q. Let $z$ be a complex number
Assertion (A) :The equation $|z - 1| - |z - i| = 1$ represents a hyperbola.
Reason (R) : The equation $|z - z_1| - |z - z_2| = k$ is a hyperbola.

Complex Numbers and Quadratic Equations Report Error

Solution:

The equation ||$z-z_1|-| z-z_2||=k$ is a hyperbola only
if $k<\left|z_1-z_2\right|$
Here $k=1 \&\left|z_1-z_2\right|=\sqrt{2} \nless 1\left\{z_1=1, z_2=i\right\}$
Reason $( R )$ is false & Assertion $( A )$ is true.

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