Find the equation of the set of all points the sum of whose distance from the points `(3,0)a n d(9,0)` is `12.`

Explanation

To find the equation of the set of all points whose sum of distances from the points \( A(3, 0) \) and \( B(9, 0) \) is 12, we can follow these steps:

### Step 1: Set up the distance equation
Let \( P(x, y) \) be any point in the plane. The distances from \( P \) to points \( A \) and \( B \) can be expressed using the distance formula:

\[ PA = \sqrt{(x - 3)^2 + (y - 0)^2} = \sqrt{(x - 3)^2 + y^2} \]
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