In this exercise, find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results.

$$x=t^2-t+2, \quad y=t^3-3 t$$

Consider the parametric equations $x=4 \cos ^2 \theta$ and $y=2 \sin \theta$.

If values of $\theta$ were selected from the interval $[\pi / 2,3 \pi / 2]$ for the table in first part, would the graph in second part be different? Explain.

Consider the parametric equations $x=4 \cos ^2 \theta$ and $y=2 \sin \theta$.

Find the rectangular equation by eliminating the parameter, and sketch its graph. Compare the graph in second part with the graph of the rectangular equation.

Consider the parametric equations $x=4 \cos ^2 \theta$ and $y=2 \sin \theta$.

Use a graphing utility to confirm your graph in previous part.

In this exercise, use a graphing utility to graph the polar equation when $e=1.5$. Identify the conic.

$$r=\dfrac{2 e}{1-e \cos \theta}$$

Consider the parametric equations $x=4 \cos ^2 \theta$ and $y=2 \sin \theta$.

Plot the points $(x, y)$ generated in the table, and sketch a graph of the parametric equations. Indicate the orientation of the graph.