Concept explainers
(a)
To explain: The meaning of a parametric curve.
(a)
Explanation of Solution
The parametric curve is defined as the set of points
Thus, a parametric curve has two separate functions for x and y coordinates, which are represented in terms of a variable t, called the parameter.
For example, a circle of radius r is defined by the parametric equations
In general, the curve with parametric equations
(b)
To explain: The method to sketch a parametric curve.
(b)
Explanation of Solution
In general, it is difficult to sketch a parametric curve that is represented by two functions.
Thus, find the values of
Sometimes, the parameter t are eliminated from
That is, it is easier to graph the equation, than working with the original formulas of x and y in terms of t.
Want to see more full solutions like this?
Chapter 9 Solutions
ESSENTIAL CALCULUS LL
- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.arrow_forwardShooting into the Wind Suppose that a projectile is fired into a headwind that pushes it back so as to reduce its horizontal speed by a constant amount . Find parametric equations for the path of the projectile.arrow_forwardCalculus with Parametric Curvesarrow_forward
- sketch the parametric curve x=e^t, y=e^-2t. Then eliminate the parameter to find a Cartesian equation for the curvearrow_forwardSketch the curve represented by the parametric equations (indicate the orientation of the curve). x=3-2t y=2+3tarrow_forwardUse a graphing utility to graph the curve represented by the parametric equations. (Indicate the orientation of the curve.) x = 2 sec(?), y = 9 tan(?)arrow_forward
- 22) I would some help to find parametric equations for the tangent line to the curvewith the given parametric equations at the specified point, please?arrow_forwardI need help with this problem and an explanation of the solution described below (This is based upon Parametric Curves):arrow_forwardWhat are plane curves and parametric equations?arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage