Jbreezy said:Not sure maybe someone else has ideas too?
Jbreezy said:Homework Statement
I have to eliminate the parameter and write in Cartesian form.
Homework Equations
y= sqrt(t +1) and y = sqrt(t-1)
The Attempt at a Solution
If you were to just go for the gusto and square it out you will end up with 0 = 2. Clearly I'm missing something here. Just stumped. I don't think the right way to go is squaring and setting them equal.
Parametric equations represent mathematical relationships between two or more variables, while standard equations represent a relationship between variables in terms of a single variable. In parametric equations, each variable is defined in terms of a third variable, called a parameter, while standard equations do not have this parameter.
The square root in these equations represents the inverse function of squaring a number. In other words, it is the function that undoes the squaring operation. In these particular equations, the square root is used to represent the positive square root of a number, as the negative square root is not typically used in parametric equations.
When these equations are graphed, they create a curve known as a parabola. The parameter t represents the x-coordinate of points on the parabola, while the y-coordinate is represented by the function value of either of the equations. As t increases, the points on the parabola move to the right, and as t decreases, the points move to the left.
The domain of these equations is all real numbers greater than or equal to 1, as the square root function is undefined for negative numbers. The range is all real numbers greater than or equal to 0, as the square root function always produces positive values.
Parametric equations are used in many fields of science and engineering, including physics, biology, and computer graphics. In particular, these equations can be used to model the motion of objects in projectile motion and to create smooth, curved lines in computer graphics. They are also used in statistical analysis and data modeling.