If origin is shifted to the point `(a,b)` then what will be the transformed equation of the curve `(x-a)^(2)+(y-b)^(2)=r^(2)` ?

Explanation

To solve the problem of transforming the equation of the curve \((x-a)^{2}+(y-b)^{2}=r^{2}\) when the origin is shifted to the point \((a,b)\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Shift of Origin**: When the origin is shifted from \((0,0)\) to \((a,b)\), the new coordinates \((X,Y)\) can be expressed in terms of the old coordinates \((x,y)\) as:
\[ x = X + a \quad \text{and} \quad y = Y + b \]
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