When Elasticity of Demand Curve is 1 at every point on the Demand Curve, this curve is known as:

The correct option is Rectangular Hyperbola.

Here is a step-by-step explanation of why this is the correct answer:

The price elasticity of demand ($E_d$) measures the responsiveness of the quantity demanded of a good to a change in its price. It is calculated as:

$E_d=\; -\frac{\%\text{Change in Quantity Demanded}}{\%\text{Change in Price}}$

When the elasticity of demand is equal to 1 (unitary elastic) at every single point along the demand curve, it implies that any percentage change in price leads to an equal percentage change in the quantity demanded in the opposite direction. Mathematically, this relation can be written in terms of total expenditure ($\text{Price}\times \text{Quantity}$). For a unitary elastic demand curve, the total expenditure remains constant at all price levels.

Let $P$ represent price and $Q$ represent quantity demanded. Since the total outlay or revenue remains constant ($C$) when elasticity is 1 at all points, we have:

$P\times Q=C$

In coordinate geometry, the equation $xy=c$ (where $c$ is a constant) represents a curve known as a rectangular hyperbola. Under this curve, the area of any rectangle formed by drawing perpendiculars from any point on the curve to the coordinate axes ($P$ and $Q$ axes) is always constant and equal to $C$.

Therefore, a demand curve with a constant price elasticity of demand equal to 1 at all points is shaped as a rectangular hyperbola.