Consider the parametric equations below. x = t², y = t⁹ (a) sketch the curve by using the parametric equations to plot points. indicate with an arrow the direction in which the curve is traced as t increases.

Solution:

x = t²

t = √x

Substituting the above in y = t⁹ we get

y = (√x)⁹

Using this equation we plot the graph below with the help of the table (also given below)

The graph above shows the direction of the curve as the value of t increases.

Consider the parametric equations below. x = t², y = t⁹ (a) sketch the curve by using the parametric equations to plot points. indicate with an arrow the direction in which the curve is traced as t increases

Summary:

The curve by using the parametric equations is plotted above in the solution and the arrows indicate the direction in which the curve is traced as t increases