Find the locus of the midpoint of the chords of the circle `x^2+y^2=a^2` which subtend a right angle at the point `(c ,0)dot`

Explanation

To find the locus of the midpoint of the chords of the circle \( x^2 + y^2 = a^2 \) that subtend a right angle at the point \( (c, 0) \), we can follow these steps:

### Step 1: Define the midpoint of the chord
Let \( P(h, k) \) be the midpoint of the chord \( AB \) of the circle. The circle's equation is \( x^2 + y^2 = a^2 \).

### Step 2: Use the property of the right angle
Since the chord \( AB \) subtends a right angle at the point \( (c, 0) \), we can use the property that the distances from \( P \) to \( A \) and \( B \) are equal to the distance from \( P \) to \( (c, 0) \).

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