SECTION 10.3 Parametric Equations and Calculus 719 Section 10.3 Parametric Equations and Calculus • Find the slope of a tangent line to a curve given by a set of parametric equations. • Find the arc length of a curve given by a set of parametric equations. • Find the area of a surface of revolution (parametric form). Slope and Tangent Lines In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters. Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface, in which case the equations are collectively called a parametric representation or parameterization (alternatively Calculas 102 Parametric Equations ???? ???????? pdf. Category Education; Show more Show less. 10 1 Curves Defined by Parametric Equations - Duration: Sal gives an example of a situation where parametric equations are very useful: driving off a cliff! If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, 9.1 Parametric Curves So far we have discussed equations in the form . Sometimes and are given as functions of a parameter. Example. Projectile Motion Sketch and axes, cannon at origin, trajectory Mechanics gives and . Time is a parameter. Given parameter . Then , are parametric equations for a curve in the -plane. Example. , Draw the curve in the set of curves that we can get from y = mx by plugging in some number for m. More generally, for any positive integer n, an n-parameter family of curves is the collection of curves we get by taking an equation involving x, y, and n other variables, provided that that family of curves cannot be represented with fewer parameters. ParametricCurves (Com S 477/577 Notes) Yan-BinJia Oct8,2019 1 Introduction Curves and surfaces are abundant with man-made objects, tools, and machines which are ubiquitous in our daily life. Engineering curves and surfaces have many applications in industry. For example, hyperbolic shapes are used on cooling towers while spiral shapes are used Section 3-3 : Area with Parametric Equations. For problems 1 and 2 determine the area of the region below the parametric curve given by the set of parametric equations. For each problem you may assume that each curve traces out exactly once from left to right for the given range of t. An implicit curve is defined by a single equation f(?,Y) = 0 and an implicit surface is defined by a single equation f(x.y,z) = 0 Thus. the curve or surface points are those that satisfy the implicit equation, so that we no longer think of curves and surfaces as the result of a mapping. We will restrict the function f to polynomials. Finding Cartesian Equations from Curves Defined Parametrically. When we are given a set of parametric equations and need to find an equivalent Cartesian equation, we are essentially "eliminating the parameter." However, there are various methods we can use to rewrite a set of parametric equations as a Cartesian equation. You lose the input information. You get the shape of the curve. And if you just want, you know, an analytical way of describing curves, you find some parametric function that does it. And you don't really care about the rate. But just to show where it might matter, I'll animate the same thing again, another function that draws the