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| Math Central | Quandaries & Queries |
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Question from will, a student: Graph and make a sketch of x = ysquared - 6y + 11 in parametric mode (hint: you need to come up with 2 parametric equations). i have already figured out that the cartesian form of the parametrics will be y = +/- sqroot(x-2) + 3, but i do not know how to produce 2 parametric equations from this. |
Hi Will,
I think you went a couple of steps to far in your calculations. It is better to leave the cartesian form as
x = (y - 3)2 + 2
Now let t = y - 3 and then this implies that x = t2 + 2. Hence the parametric equations are
x = t2 + 2
y = t + 3
Now you can use these equations to sketch the graph. Substitute various values of t, generate values of x and y and then plot them. I would keep track with a table
| t | x | y |
|---|---|---|
| 0 | 2 | 3 |
| 1 | 3 | 4 |
| -1 | 3 | 2 |
| 2 | 6 | 5 |
| . | . | . |
Penny
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