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Question: 5 the following problem was first posed in 1638 and...

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5) The following problem was first posed in 1638, and worked on, amongst others by Descartes, Fermat, Leibniz and Jakob Bernoulli until 1693; so you should have no trouble solving it in a week! Its a geometry problem; find the formula of a curve y(x) such that the length of the segment of the tangent to the curve between the curve and the x-axis is equal to a constant a at all points on the curve. We draw a right-angled triangle with base on the x-axis, and height y and hypotenuse d 2 21/2 from which we see that the differential equation of the curve must be dx where a > 0 is an arbitrary constant (the length of the tangent segment) Find the solution in implicit form. Can you write the solution as x-g(y), that is x equal to a function of y? Hint: The substitution z-a2-v2 may be useful to evaluate one of the integrals that arises.]

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