- #1
baokhuyen
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Homework Statement
how can we eliminate the parameter of these functions:
x= t-2
y= t^2 +1
and sketch its curve
Homework Equations
The Attempt at a Solution
I can't find the relations between these 2 functions
Parametric equations are a set of equations that express a set of variables as functions of one or more independent variables, known as parameters. These equations are often used to describe curves and surfaces in mathematics and physics.
To solve parametric equations, you need to first eliminate the parameter by solving one of the equations for the parameter in terms of the other variables. Then, substitute this expression into the other equation to get an equation with only one variable. Finally, solve for this variable to get the solution to the parametric equations.
Yes, parametric equations can be graphed by plotting points on a coordinate plane. The independent variable is usually graphed on the x-axis and the dependent variable on the y-axis. The resulting graph will be a curve or surface.
Sketching the curve for parametric equations allows you to visualize the shape of the curve and better understand its behavior. It can also help in determining the domain and range of the curve and identifying any special points or characteristics.
Yes, there are a few techniques that can make sketching parametric curves easier. These include plotting points for various values of the parameter, finding the slope of the curve at specific points, and using symmetry to help with the sketching process.