Prove that the curves `x y=4` and `x^2+y^2=8` touch each other.

Explanation

To prove that the curves \( xy = 4 \) and \( x^2 + y^2 = 8 \) touch each other, we will follow these steps:

### Step 1: Find the points of intersection
We start with the equations of the curves:
1. \( xy = 4 \) (Equation 1)
2. \( x^2 + y^2 = 8 \) (Equation 2)

From Equation 1, we can express \( y \) in terms of \( x \):
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