The difference of the distances of variable point from two given points (3,0) and (-3,0) is 4. Find the locus of the point.

Explanation

To find the locus of a point \( P(h, k) \) such that the difference of its distances from the points \( S(3, 0) \) and \( S'(-3, 0) \) is 4, we can follow these steps:

### Step 1: Set up the distance equations
The distance from point \( P(h, k) \) to point \( S(3, 0) \) is given by:
\[ d_1 = \sqrt{(h - 3)^2 + (k - 0)^2} = \sqrt{(h - 3)^2 + k^2} \]
The distance from point \( P(h, k) \) to point \( S'(-3, 0) \) is given by:
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