Chapter 10, Problem 1RCC

(a)

To determine

To Find: The parametric curve definition

Explanation of Solution

Write the definition of the parametric curve.

The parametric curve is defined as the set of points in the plane (the parametric equations of $x=f\left(t\right)$ and $y=g\left(t\right)$) where the variable $t$ increases, the increase in parameters of $x$ and $y$ will produce parametric curve in the plane.

(b)

To determine

To define: The sketch of a parametric curve.

Explanation of Solution

Define the sketch the parametric curve.

Here, $\frac{dy}{dx}$ is the slope of tangent of a parametric curve which can be represented as the function of $t$.

The expression is given as $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}$.

Therefore, for determining the tangent of the curve, the above derivative equation is to be evaluated to define the parametric curve.