Prove that the curves `x=y^2`and `x y = k` cut at right angles* if `8k^2=1`.

Explanation

To prove that the curves \( x = y^2 \) and \( xy = k \) cut at right angles if \( 8k^2 = 1 \), we will follow these steps:

### Step 1: Find Points of Intersection
We have two curves:
1. \( x = y^2 \) (Curve 1)
2. \( xy = k \) (Curve 2)

To find the points of intersection, we substitute \( x = y^2 \) into the second equation \( xy = k \):
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