Then substitute this result for the parameter in the other parametric equation and simplify. If you are given parametric equations, you can sometimes create a cartesian equation by eliminating the parameter. Curve sketching can be less tedious by converting the two parametric equations into one rectangular equation. Mei core 4 parametric equations chapter assessment 1. Sketch the parametric equations by eliminating the. Parametric equations eliminating the parameter finding a rectangular equation that represents the graph of a set of parametric equations is called eliminating the parameter. Eliminating the parameter to graph parametric equations, ex 1. Check your work by first graphing the parametric equations on your calculator than graphing the cartesian equations also on your calculator to see if they match.
In mathematics this third quantity is called a parameter. Substitute the expression for t in the other parametric equation. Eliminate the parameter to write the parametric equations as a rectangular equation. Instead of one equation relating say, x and y, we have two equations, one relating x with the parameter. Eliminate the parameter in the following set of parametric equations and write as a cartesian equation. Use point plotting to graph plane curves described by parametric equations. Given the parametric equations below, eliminate the parameter t to obtain an equation for y as a function of x xt e4t yt e2t yx get more help from chegg. Graphing parametric equations and eliminating the parameter ex. Enter your answers as a commaseparated list of equations. Eliminate the parameter, set up the parametric equation for to solve the equation for. Eliminating angle parameters in a parametric equation the parameter can represent anything including an angle. This method is referred to as eliminating the parameter.
Read online parametric equations the student room book pdf free download link book now. The result of eliminating the parameter will be a rectangular equation whose graph is more easily recognizable. Just as with nonangle parameters, when the parameter is an angle. Find a rectangular equation for a curve defined parametrically. Make a table of values and sketch the curve, indicating the direction of your graph. Sketch the plane curve represented by the parametric equations by eliminating the parameter. To do this we will square both parametric equations to get. Calculus ii parametric equations and curves practice. Removing the parameter in parametric equations video. Parametric equations introduction, eliminating the.
Here we explore the use of a parameter t in the description of curves. Removing the parameter in parametric equations example 2 our mission is to provide a free, worldclass education to anyone, anywhere. For problems 1 6 eliminate the parameter for the given set of parametric equations, sketch the graph of the parametric curve and give any limits that might exist on x and y. To find the cartesian equation of a curve from its parametric equations you need to eliminate the parameter.
1403 6 252 221 991 785 150 110 168 928 380 290 743 1009 898 692 1133 1608 944 308 1568 794 157 1121 76 1404 1324 590 879 54 1254 532 1526 1551 284 365 1488 1357 389 688 149 858 966 1052 735 983 526 602