Chapter 10, Problem 5PS

(a)

To determine

To calculate: The rectangular equation of the Strophoid if

$\begin{array}{l}x\left(t\right)=\frac{1-t^2}{1+t^2}\\ y\left(t\right)=\frac{t\left(1-t^2\right)}{1+t^2}\end{array}$

(b)

To determine

To calculate: The polar equation of the Strophoid if

$\begin{array}{l}x\left(t\right)=\frac{1-t^2}{1+t^2}\\ y\left(t\right)=\frac{t\left(1-t^2\right)}{1+t^2}\end{array}$

(c)

To determine

To graph: The equation of strophoid if

$\begin{array}{l}x\left(t\right)=\frac{1-t^2}{1+t^2}\\ y\left(t\right)=\frac{t\left(1-t^2\right)}{1+t^2}\end{array}$

(d)

To determine

To calculate: The equation of two tangent lines at the origin if

$\begin{array}{l}x\left(t\right)=\frac{1-t^2}{1+t^2}\\ y\left(t\right)=\frac{t\left(1-t^2\right)}{1+t^2}\end{array}$

(e)

To determine

To calculate: The point at which the tangent lines are horizontal if

$\begin{array}{l}x\left(t\right)=\frac{1-t^2}{1+t^2}\\ y\left(t\right)=\frac{t\left(1-t^2\right)}{1+t^2}\end{array}$