Prove that `|Z-Z_1|^2+|Z-Z_2|^2=a` will represent a real circle [with center `(|Z_1+Z_2|^//2+)` ] on the Argand plane if `2ageq|Z_1-Z_1|^2`

Explanation

To prove that \( |Z - Z_1|^2 + |Z - Z_2|^2 = \alpha \) represents a real circle in the Argand plane with center \( \frac{Z_1 + Z_2}{2} \) under the condition \( 2\alpha \geq |Z_1 - Z_2|^2 \), we will follow these steps:

### Step 1: Expand the expressions
Start with the given equation:
\[ |Z - Z_1|^2 + |Z - Z_2|^2 = \alpha \]
Using the definition of modulus, we can expand the left-hand side:
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