The sum of the squares of the distances of a moving point from two fixed points `(a ,0)a n d(-a ,0)` is equal to a constant quantity `2c^2dot` Find the equation to its locus.

Explanation

To find the equation of the locus of a moving point such that the sum of the squares of its distances from two fixed points \( (a, 0) \) and \( (-a, 0) \) is equal to a constant \( 2c^2 \), we can follow these steps:

### Step 1: Define the moving point and fixed points
Let the moving point be \( P(x, y) \).
The fixed points are \( A(a, 0) \) and \( B(-a, 0) \).

### Step 2: Write the distances from the moving point to the fixed points
Using the distance formula, we can express the distances from point \( P \) to points \( A \) and \( B \):
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