The curvature of a plane parametric curve x = f(t), y = g(t) is $ \kappa = \dfrac{|\dot{x} \ddot{y} - \dot{y} \ddot{x}|}{[\dot{x}^2 + \dot{y}^2]^{3/2}}$ where the dots indicate derivatives with respect to t. Use the above formula to find the curvature. x = 6et cos(t), y = 6et sin(t)

The curvature is modelled by .

Step-by-step explanation:

The equation of the curvature is:

The parametric componentes of the curve are:

and

The first and second derivative associated to each component are determined by differentiation rules:

First derivative

and

and

Second derivative

Now, each term is replaced in the the curvature equation:

And the resulting expression is simplified by algebraic and trigonometric means:

The curvature is modelled by .