What does the equation `(a-b)(x^2+y^2)-2a b x=0` become if the origin is shifted to the point `((a b)/(a-b),\ 0)` without rotation?

Explanation

To solve the equation \((a-b)(x^2+y^2)-2abx=0\) after shifting the origin to the point \(\left(\frac{ab}{a-b}, 0\right)\) without rotation, we will follow these steps:

### Step 1: Define the new coordinates
We shift the origin from \((0,0)\) to \(\left(\frac{ab}{a-b}, 0\right)\). Let:
- \(h = \frac{ab}{a-b}\)
- The new coordinates will be defined as:
\[
X = x - h \quad \text{and} \quad Y = y
...