Show that the curves `x y=a^2a n dx^2+y^2=2a^2` touch each other

Explanation

To show that the curves \( xy = a^2 \) and \( x^2 + y^2 = 2a^2 \) touch each other, we need to follow these steps:

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

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