How to find the derivative of a parametric curve?

x(t) = t2 − 3, y(t) = 2t − 1, for − 3 ≤ t ≤ 4 x(t) = 2t + 1, y(t) = t3 − 3t + 4, for − 2 ≤ t ≤ 2 x(t) = 5cost, y(t) = 5sint, for 0 ≤ t ≤ 2π

https://www.storyofmathematics.com/parametric-curves

How do you graph a parametric equation?

parametric equations are for what i know, are better thought as lines. Be on 2D, 3D or 100Dimensions. So starting by the way to graph, to each value of the common parameter, which usually is “t”, you plug it on each equation that describes a coordinate and it will give you a number. mark each point on the plane and draw the line. Ps.:

https://www.quora.com/How-do-you-find-where-a-parametric-equation-crosses-itself-How-do-you-graph-a-parametric-equation

How to convert parametric equations into Cartesian equations?

Key Concepts Parameterizing a curve involves translating a rectangular equation in two variables, x x and y, y, into two equations in three variables, x, y, and t. ... Sometimes equations are simpler to graph when written in rectangular form. ... To eliminate t, t, solve one of the equations for t, t, and substitute the expression into the second equation. ... More items...

https://www.quora.com/How-can-you-convert-parametric-equations-into-Cartesian-equations

How do you eliminate a parameter from a parametric equation?

Parametric Equations: Eliminating Parameters Solve one of the parametric equations for the parameter x = 1 t + 1 2 Original 1 x = t + 1 2 Take inverse 1 x ... Substitute the resulting expression for the parameter into the other parametric equation and simplify. ... Determine the domain of the rectangular equation. ... Sketch the curve.

https://www.softschools.com/math/pre_calculus/parametric_equations_eliminating_parameters/