Parametric Equations

Parametric Equations: Level 2 Challenges


The curve described parametrically by {x=t2+ty=t2t \begin{cases} x=t^{2}+t \\ y=t^{2}-t \end{cases} represents which of the following shapes?

The parametric equations for the curve shown are {x=cos(t)y=sin(t)z=? \begin{cases} x = \cos(t) \\ y = \sin(t) \\ z = \text{?} \end{cases} where tt ranges over (0,20)(0, 20). Which function could zz be equal to?

{x=ety=e2t1 \begin{cases} x = e^t \\ y = e^{2t} - 1 \end{cases}

What is the shape of the curve described by the above parametric equation?

A point (x,y)\left( x,y \right) moves counterclockwise along the unit circle at constant angular speed ω\omega . Describe the motion of the point (2xy,y2x2)\left( -2xy, { y }^{ 2 }-{ x }^{ 2 } \right) .

Two clowns, Twinkle and Jingle, are throwing pies at each other. Twinkle throws a pie toward Jingle from 500 500 centimeters away. Its flight path is given by parametric equations {x=100ty=80t16t2 \begin{cases} x &=& 100t \\ y &=& 80t - 16t^2 \end{cases} where tt is time in seconds.

Two seconds later Jingle launches an interceptor pie from his location with the flight path {x=500500(t2)y=K(t2)16(t2)2 \begin{cases} x &=& 500 - 500(t-2) \\ y &=& K(t-2) - 16(t-2)^2 \end{cases} Find the value of KK which will guarantee that the interceptor pie will hit its target (the pie thrown by Twinkle).


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