Which variable is typically used as the parameter in parametric equations?

Given x(t) = 2cos(t), y(t) = 5sin(t), for t in [0, 2π], what is the rectangular equation and what geometric figure does it represent?

A clock has a minute hand of length $10$ inches that makes one full revolution every $3600$ seconds. Let $(x,y)$ be the position of the tip relative to the clock center, and take $t$ in seconds with $t=0$ when the tip points to the $3$ o'clock position. Write parametric equations $x\left(t\right)$ and $y\left(t\right)$ for the motion.

What is the derivative of y(t) = 5t^4 with respect to t?

Given x(t) = t^2 and y(t) = t^3, find dy/dx in terms of t.

Find the arc length of the curve x(t) = 3t, y(t) = 4t for t in [0, 2].

In the polar coordinate system, what does the variable r represent?

Convert the polar point (4, π/3) to rectangular coordinates.

Find all the non-origin intersection points (in polar coordinates) of the curves $r=3\cos \theta$ and $r=1+2\cos \theta$ for $\theta$ in $[0,2\pi )$.

Find the slope of the tangent line to the polar curve $r=1+2\sin \theta$ at the point with $\theta =\frac{\pi }{2}$.

Compute the area enclosed by the polar curve $r=\sqrt{2\cos \theta }$.

Find the arc length of the polar curve $r\left(\theta \right)=3\cos \theta +4\sin \theta$ for $0\le \theta \le \pi$.

If a circle is graphed with its center at (0,0) and passes through the point (0,4), what is its radius?

Find the equation of the tangent line to the curve $\frac{x^2}{25}+\frac{y^2}{9}=1$ at the point $(4,\frac{9}{5})$. Write your answer in slope-intercept form.