Waste less time on Facebook — follow Brilliant.
×

Parametric Equations

As a particle moves, its position can often be written in terms of time. Systems like these can be modeled with parametric equations, which cleverly write coordinates in terms of a parameter.

Challenge Quizzes

Basic Shapes

         

Which of the following is the curve defined by the parametric equations \[x=4\sin t, \quad y=8\cos t,\] assuming that \(x_1=y_1=4\) and \(x_2=y_2=8?\)

If \((a,b)\) is the center and \(r\) is the radius of the circle defined by the parametric equations \[x=6\cos 6t, \quad y=6\sin 6t, \quad 0 \leq t \leq 2\pi, \] what is the value of \(a+b+r\)?

Which of the following is the curve defined by the parametric equations \[x=6\sin t, \quad y=5\sin^2 t ?\]

What shape does the following parametric equation describe:

\[ x = 3 \cos ^2 \theta, y = 6 \sin^2 \theta. \]

Consider the ellipse defined by the parametric equations \[x=12\cos t, \quad y=4\sin t,\] where \(0 \leq t \leq 2\pi\). If the length of the major axis is \(a\) and the length of the minor axis is \(b\), what is the value of \(a+b\)?

×

Problem Loading...

Note Loading...

Set Loading...