Exercises

01

Sketch the curve given by $(x,y)=(2t-4,3+t^2)$.

02

Describe the parametric curve $(x,y)=(2t-4,3+t^2)$ as the graph of a function.

03

Consider the curve $(50t,100t-5t^2)$. Find the point on this curve with largest $y$-value.

04

[Already done in class.]
Points satisfying ${\left(\frac{x}{2}\right)}^2+{\left(\frac{y}{5}\right)}^2=1$ lie on an ellipse. Find a parametric curve that covers this ellipse.

05

Find a parametric curve that is a line passing through $(3,-2)$ with slope $m=4$.

06

Eliminate $t$ to find an equation satisfied by $x,y$ alone for the following two parametric curves:
a. $(x,y)=(t^2-3,t+2)$
b. $(x,y)=(\csc (t),\cot (t))$

07

Describe the image of the curve parametrized by $(x,y)=(\sin (t),{\cos }^2(t))$.

08

One particle has position $(x,y)=(t+5,t^2+4t+6)$, a second particle has position $(2t+1,2t+6)$. Calculate the two points of intersection of the image curves determined by these formulas. Do the particles collide at those intersection points?