Question
Investigate the family of curves defined by the parametric equations $ x = t^2 $, $ y = t^3 - ct $. How does the shape change as $ c $ increases? Illustrate by graphing several members of the family.
Step 1
The equations are $x = t^2$ and $y = t^3 - ct$. Here, $t$ is the parameter and $c$ is a constant that can vary. Show more…
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$$ \begin{array}{l}{\text { Investigate the family of curves defined by the parametric }} \\ {\text { equations } x=t^{2}, y=t^{3}-c t . \text { How does the shape change }} \\ {\text { as } c \text { increases? Illustrate by graphing several members of the }} \\ {\text { family. }}\end{array} $$
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Investigate the family of curves defined by the parametric equations $x=t^{2}, y=t^{3}-c t .$ How does the shape change as $c$ increases? Illustrate by graphing several members of the family.
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