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?

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- Dec 21st 2012, 07:14 AMPStudent175Converting from parametric from to implicit
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? - Dec 21st 2012, 09:39 AMHallsofIvyRe: Converting from parametric from to implicit
You are saying that x= s^2- s+ 1, y= s^2+ s+ 1. You want to eliminate s from those two equations. You could, for example, solve each equation for s, using the quadratic formula, then set the two equal.

- Dec 21st 2012, 06:29 PMSorobanRe: Converting from parametric from to implicit
Hello, PStudent175!

I have a solution, but it's quite awkward.

Quote:

Add [1] and [2]: .

. . . . . . . . . . . . .

Substitute into [2]: .

. . . . . . . . . . . . . . .

. . . . . . . . .

Square: .

I'll letclean it up . . .*you*

- Dec 21st 2012, 07:49 PMzzephodRe: Converting from parametric from to implicit
- Dec 22nd 2012, 07:42 AMPStudent175Re: Converting from parametric from to implicit
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! - Dec 22nd 2012, 11:47 AMSorobanRe: Converting from parametric from to implicit
Hello again, PStudent175!

Quote:

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).

- Dec 22nd 2012, 08:04 PMzzephodRe: Converting from parametric from to implicit