If `z=x+i y ,` then show that `z bar z +2(z+ bar z )+a=0` , where `a in R ,` represents a circle.

Explanation

Let's solve the problem step by step.

### Given:
Let \( z = x + iy \).

We need to show that the equation \( z \bar{z} + 2(z + \bar{z}) + a = 0 \) represents a circle, where \( a \in \mathbb{R} \).

### Step 1: Find \( z \bar{z} \)
...