Hi,
I am stuck on converting from parametric form to implicit.
For example, if the curve is:
c = (s^2-s+1, s^2+s+1)
How should I express as implicit representation?
Hello, PStudent175!
I have a solution, but it's quite awkward.
Add [1] and [2]: .
. . . . . . . . . . . . .
Substitute into [2]: .
. . . . . . . . . . . . . . .
. . . . . . . . .
Square: .
I'll let you clean it up . . .
Perfect, thanks a lot that was very useful.
For the next question it is:
x = (a-t) / (a+t)
y = (t) / (a+t)
And I have tried the same method by adding together to get x+y= a / a+t but am not really sure to go from there?
Do you know of any resources that has information on this topic as I haven't been taught it yet at university.
Thanks again for the help!
Hello again, PStudent175!
I could find no "clever" way to eliminate the parameter.
Solve [2] for
. .
Substitute into [1]: .
Muliply by
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Interesting observation . . .
The graph is the straight line
. . with a "hole" at (-1, 1).