A curve is given parametrically by x = 3 + 9e tan acos 0, where a is a constant in the interval (0, π/2) and is a real-valued parameter. y = 4 + 9e tan asin 0. In this example, we can consider the whole curve by allowing the intrinsic angle to take any real value. Find an expression for tan in terms of 0 and a. Now, find an expression for the arclength s in terms of and a, choosing a sign convention such that s is positive and setting for convenience s→→0 as →∞0₁ Finally, combine the previous two results to find a relation between s and. From the form of this relation (and/or the original parametric equations) what shape must the curve have? (Choose one) OA circle OA spiral OA cycloid ONone of the other options OA straight line
A curve is given parametrically by x = 3 + 9e tan acos 0, where a is a constant in the interval (0, π/2) and is a real-valued parameter. y = 4 + 9e tan asin 0. In this example, we can consider the whole curve by allowing the intrinsic angle to take any real value. Find an expression for tan in terms of 0 and a. Now, find an expression for the arclength s in terms of and a, choosing a sign convention such that s is positive and setting for convenience s→→0 as →∞0₁ Finally, combine the previous two results to find a relation between s and. From the form of this relation (and/or the original parametric equations) what shape must the curve have? (Choose one) OA circle OA spiral OA cycloid ONone of the other options OA straight line
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A curve is given parametrically by
x = 3 + 9e tan acos 0,
where a is a constant in the interval (0, π/2) and is a real-valued parameter.
y = 4 + 9e tan asin 0.
In this example, we can consider the whole curve by allowing the intrinsic angle to take any real value. Find an expression for tan in
terms of 0 and a.
Now, find an expression for the arclength s in terms of and a, choosing a sign convention such that s is positive and setting for
convenience s→→0 as →∞0₁
Finally, combine the previous two results to find a relation between s and. From the form of this relation (and/or the original parametric
equations) what shape must the curve have? (Choose one)
OA circle
OA spiral
OA cycloid
ONone of the other options
OA straight line
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