Verify Unit length to y-axis from Tractrix Curve

In summary, the problem discussed is number 6 and involves finding the length of a curve using the tangent line at a given point. The approach suggested is to find the tangent line at t=0 and show that it has a length of 1 from y=0 to the point on the curve. It is unclear whether the solution would involve subtracting the two points or using the formula for length involving the integral of the absolute value of the derivative of γ(t). The asker is seeking assistance with this problem.
  • #1
MxwllsPersuasns
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Homework Statement


The problem is described in the picture I've attached. It is problem number 6.

Homework Equations


Tangent line of a curve
Length of a curve

The Attempt at a Solution


I don't know why I'm so confused on what seems like it should be a relatively straightforward problem, but I am. I guess I would approach this problem by finding the tangent line at a point (say t=0) (though I forget the procedure to do that exactly) and then basically just show that the tangent line has length 1 from y = 0 basically?
- Also would I just like subtract the two points (i.e., the point on the curve where there is a tangent line and then the y-axis (y = 0)) or would it require the use of the formula for length namely the integral of the absolute value of the derivative of γ(t) from the y-axis to the point on the curve?

Any help with this would be greatly appreciated!
 

Attachments

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  • #2
It would help if you would type the statement of the problem instead of posting an illegible image.
 

FAQ: Verify Unit length to y-axis from Tractrix Curve

1. What is a tractrix curve?

A tractrix curve is a mathematical curve that describes the path traced by a point on a moving object as it is pulled along by a string or chain of fixed length. It is also known as the pursuit curve.

2. How is the unit length to y-axis measured from a tractrix curve?

The unit length to y-axis from a tractrix curve is measured by finding the distance between the point where the curve intersects the y-axis and the origin (0,0) of the coordinate system.

3. Why is it important to verify the unit length to y-axis from a tractrix curve?

Verifying the unit length to y-axis from a tractrix curve is important because it allows us to accurately determine the length of the curve and make precise calculations based on its properties. It also ensures that the curve is consistent with the mathematical model and can be used for further analysis or application.

4. Can the unit length to y-axis from a tractrix curve vary?

Yes, the unit length to y-axis from a tractrix curve can vary depending on the specific curve and its parameters. This is because the shape and properties of the curve are affected by the length of the string or chain and the starting position of the moving object.

5. How can the unit length to y-axis from a tractrix curve be calculated?

The unit length to y-axis from a tractrix curve can be calculated using mathematical equations and formulas that describe the curve. It can also be measured using tools such as a ruler or a graphing software.

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