A curve is given parametrically by x = 1 + 7e tan a cos 0, y...

 

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A curve is given parametrically by x = 1 + 7e tan a cos 0, y = 5 + 7e tan a sin 0. where a is a constant in the interval (0, /2) and is a real- valued parameter. In this example, we can consider the whole curve by allowing the intrinsic angle y to take any real value. Find an expression for tan y in terms of 0 and a. Now, find an expression for the arclength s in terms of 0 and a, choosing a sign convention such that s is positive and setting for convenience s 0 as 0-0. Finally, combine the previous two results to find a relation between s and y. From the form of this relation (and/or the original parametric equations) what shape must the curve have? (Choose one) A curve is given parametrically by x = 1 + 7e tan a cos 0, y = 5 + 7e tan a sin 0. where a is a constant in the interval (0, /2) and is a real- valued parameter. In this example, we can consider the whole curve by allowing the intrinsic angle y to take any real value. Find an expression for tan y in terms of 0 and a. Now, find an expression for the arclength s in terms of 0 and a, choosing a sign convention such that s is positive and setting for convenience s 0 as 0-0. Finally, combine the previous two results to find a relation between s and y. From the form of this relation (and/or the original parametric equations) what shape must the curve have? (Choose one)

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ANSWER To find an expression for tan y we can use the given equations x 1 7e0 tan a cos 0 y 5 7e0 ta... View the full answer