Y=2x+ 1 Let X=T be substituted on the left to get Y=2T+ 1, which is the parametric equation.
Similarly, in the second equation, X = T and Y = 9/T are parametric equations.
So is the third one.
The fourth is x = cos t y = sin t
This is the fourth parameter equation.
Like the fourth formula, if you have experience, you will know that you want to use trigonometric substitution as a conditioned reflex.
The first three parameter equations are all flexible, and you can also set x=2t.
How to set the parameters depends on how to set the parameters in the problem and how to calculate them conveniently, that is to say, their parameter equations are not unique.
As for the parametric equation, it is original. 、
As long as X and Y are written as a parameter-independent equation at the same time (excluding parameters), it is ok. In fact, returning to the ordinary equation is the process of eliminating parameters.
For example, x=cos t
Y = Sint
This parametric equation
What is the relationship between them? I found that x 2+y 2 =1,which is the ordinary equation.
Another example is x = 2ty = 3t 2+5.
This parametric equation
t=x/2
Substitute t in y, Y = 3 * (x 2/4)+5. This is an ordinary equation. Just simplify it.
There is no fixed formula for the specific parameter elimination method.
One depends on observation and the other on experience. But there are many simpler alternatives.