Calculus
Which of the following best describes a parametric equation?
Given x(t) = t - 2 and y(t) = 3t + 1, eliminate the parameter t to find the rectangular equation relating x and y.
Given x(t) = 3cos(t), y(t) = 4sin(t), eliminate t using a Pythagorean identity to obtain a rectangular equation.
Given the parametric equations x=3t x = 3t and y=2t+1 y = 2t + 1 , for −6≤t≤6-6 \(\leq\) t \(\leq\) 6, eliminate the parameter to find an equation relating xx and yy. Then, describe the curve represented by this equation.
For the parametric curve given by x=2sintx=2\(\sin\) t, y=5costy=5\(\cos\) t, find dydx\(\dfrac{dy}{dx}\) in terms of tt and evaluate it at t=πt=\(\pi\).