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# curve queestion watch

1. If I am given curve
I...
So, you have z=h(y), and z=g(x).

Since you have a diagram plotting x against y, do you have a function for that, or can you easily derive one?
3. (Original post by ghostwalker)
So, you have z=h(y), and z=g(x).

Since you have a diagram plotting x against y, do you have a function for that, or can you easily derive one?
Thank you for your reply, I can try and work it out.
Can you check if this is correct please?
Looks good.

5. (Original post by ghostwalker)
Looks good.

Thank you sir, for your verification.

Am I able to ask you what do I do now please?
Thank you sir, for your verification.

Am I able to ask you what do I do now please?
Well you now have x and y as functions of a parameter t, and it just remains to bring z into the picture.

You say you have z as a function of x or y - which to be honest, I find rather odd given the x-y plot. I would have thought z depended on both x and y. Is that not the case?
7. (Original post by ghostwalker)
Well you now have x and y as functions of a parameter t, and it just remains to bring z into the picture.

You say you have z as a function of x or y - which to be honest, I find rather odd given the x-y plot. I would have thought z depended on both x and y. Is that not the case?
No it is both x and y. I just articulate poorly.

So if z is a function of x and y do I try to solve by equating both z terms together and then solving?
No it is both x and y. I just articulate poorly.

So if z is a function of x and y do I try to solve by equating both z terms together and then solving?
I think I'd like to see the two diagrams and functions you've been given.

I'd expect z=h(x,y), rather than z=f(x) and z=g(y)
9. (Original post by ghostwalker)
I think I'd like to see the two diagrams and functions you've been given.

I'd expect z=h(x,y), rather than z=f(x) and z=g(y)
...
I see now. The equations you've been given relate to the cross-section of the elliptical cone on which the curve lies and not to the curve iteself.
do you need me to take the image again

If we consider the x-z diagram, and the points where the curve touches the line on the right, the x value equals the t value (cos(t) = 1) and we have z=3t/pi

If we consider the y-z diagram and the points where the curve touches the line on the right the y values is 2t and we have z=3t/pi, again.

I'd hazard a guess that z=3t/pi is our value for z in terms of the parameter t, and hence the parameterisation of the line becomes (t cos(t), 2t sin(t), 3t/pi)

Since these diagrams seem to indicate that the envelope for z=constant is an ellipse, we could just check that our parameterisation conforms to that.

Edit: Last post for today.
12. (Original post by ghostwalker)

If we consider the x-z diagram, and the points where the curve touches the line on the right, the x value equals the t value (cos(t) = 1) and we have z=3t/pi

If we consider the y-z diagram and the points where the curve touches the line on the right the y values is 2t and we have z=3t/pi, again.

I'd hazard a guess that z=3t/pi is our value for z in terms of the parameter t, and hence the parameterisation of the line becomes (t cos(t), 2t sin(t), 3t/pi)

Since these diagrams seem to indicate that the envelope for z=constant is an ellipse, we could just check that our parameterisation conforms to that.

Edit: Last post for today.
Thank you so much for this - kind of looks like an Archimdean Spiral.

13. (Original post by ghostwalker)

If we consider the x-z diagram, and the points where the curve touches the line on the right, the x value equals the t value (cos(t) = 1) and we have z=3t/pi

If we consider the y-z diagram and the points where the curve touches the line on the right the y values is 2t and we have z=3t/pi, again.

I'd hazard a guess that z=3t/pi is our value for z in terms of the parameter t, and hence the parameterisation of the line becomes (t cos(t), 2t sin(t), 3t/pi)

Since these diagrams seem to indicate that the envelope for z=constant is an ellipse, we could just check that our parameterisation conforms to that.

Edit: Last post for today.
hi ghostwalker, my friend said to use the helix, with its parametric equations. Do you know if I can do it this way too? The way you did it seems cleaner and makes more sense imo.
hi ghostwalker, my friend said to use the helix, with its parametric equations. Do you know if I can do it this way too? The way you did it seems cleaner and makes more sense imo.
Well your curve isn't a helix, though you could use that as a starting point, and you'd end up with the same parameterisation, I suspect. Depends what they did.

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