Find the locus of the middle points of the chords of the parabola `y^(2) = 4x` which touch the parabola `x^(2) = -8y`.

Explanation

To find the locus of the midpoints of the chords of the parabola \( y^2 = 4x \) that touch the parabola \( x^2 = -8y \), we will follow these steps:

### Step 1: Understand the Parabolas
The first parabola is \( y^2 = 4x \), which opens to the right. The second parabola is \( x^2 = -8y \), which opens downwards.

### Step 2: Equation of the Chord
For a parabola \( y^2 = 4ax \), the equation of the chord with midpoint \( (h, k) \) can be expressed as:
\[
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