A variable circle passes through the point `A(a ,b)` and touches the x-axis. Show that the locus of the other end of the diameter through `A` is `(x-a)^2=4b ydot`

Explanation

To solve the problem step by step, we will derive the required equation for the locus of the other end of the diameter through point \( A(a, b) \) of the circle that touches the x-axis.

### Step 1: Understand the Circle's Properties
A circle that touches the x-axis has its center at some point \( (h, k) \) where the y-coordinate \( k \) is equal to the radius \( r \) of the circle. Therefore, we can write:
\[ k = r \]

### Step 2: General Equation of the Circle
The general equation of a circle in terms of its center \( (h, k) \) and radius \( r \) is given by:
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