Here’s why:

A rectangular hyperbola shaped demand curve is a specific type of demand curve where the product of price and quantity demanded remains constant across all points on the curve. This constant product translates to a unitary price elasticity at every point.
Unitay elasticity means a 1% change in price leads to a 1% change in quantity demanded in the opposite direction.
The slope of a demand curve at a point indicates the responsiveness of quantity demanded to price changes. In a rectangular hyperbola, the slope keeps changing along the curve ( steeper at higher prices, flatter at lower prices).
However, despite the changing slope, the underlying concept of a constant product between price and quantity ensures a constant unitary elasticity throughout the curve.
So, while the slope varies, the price elasticity remains consistently equal to 1.