Find the locus of the point `(t^2-t+1,t^2+t+1),t in Rdot`

Explanation

To find the locus of the point \((t^2 - t + 1, t^2 + t + 1)\) as \(t\) varies over the real numbers, we will follow these steps:

### Step 1: Define the Coordinates
Let \(x = t^2 - t + 1\) and \(y = t^2 + t + 1\).

### Step 2: Express \(y\) in Terms of \(x\)
We can express \(y\) in terms of \(x\) by eliminating \(t\). First, we can rewrite \(y\) as:
\[
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