Solving Parametric Equations for y=√x

In summary, three sets of parametric equations for y=√x are x=t y=√t, x=3t y=√3t, and x=t+3 y=√t+3. These equations may seem easy, but there is room for creativity in finding alternative solutions.
  • #1
SPhy
25
0
Even problem in 2nd semester calc book.

Homework Statement



Come up with three sets of PE for y=√x


The Attempt at a Solution



This is the first time in my math education that I've come across parametric equations where I am required to give 2 or more sets.

The first one:

x=t y=√t

Second:

x=3t y=√3t

Third:

x=t+3 y=√t+3

----

My approach seems too easy; I have a sense my intuition on parametric equations is lacking, but any help would be appreciated!
 
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  • #2
There is nothing wrong with your answers. You could be more creative if you want to. For example if you let ##x=t^2## and ##y=~?##.
 

1. What are parametric equations?

Parametric equations are a set of equations that express the coordinates of a point on a curve as a function of one or more independent parameters, rather than just the variables x and y.

2. How do you solve parametric equations for y=√x?

To solve parametric equations for y=√x, you need to eliminate the parameter and express y solely in terms of x. To do this, you can square both sides of the equation, which will result in x = y². Then, you can take the square root of both sides to get y = ±√x.

3. What is the relationship between parametric equations and rectangular equations?

Parametric equations and rectangular equations are two different ways to represent a curve on a coordinate plane. Parametric equations use parameters to express the coordinates of a point, while rectangular equations use variables x and y. Both forms can be used to represent the same curve, but parametric equations may be more useful in certain situations, such as when dealing with curves that are not easily expressed in terms of x and y.

4. Can parametric equations be graphed?

Yes, parametric equations can be graphed. Each set of parametric equations represents a point on a curve, so by plotting multiple points, you can graph the curve represented by the equations. This can be done using a graphing calculator or by hand.

5. What are some real-world applications of solving parametric equations for y=√x?

Solving parametric equations for y=√x can be used in various fields such as engineering, physics, and economics. For example, in engineering, parametric equations can be used to model the trajectory of a projectile, and solving for y=√x can help determine the height of the projectile at a given time. In economics, parametric equations can be used to analyze supply and demand curves, and solving for y=√x can help determine the equilibrium price and quantity.

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