A parametric curve of the form x = a cot t + b cos t , y = a + b sin t 0 < t < 2 π is called a conchoid of Nicomedes (see the accompanying figure for the case 0 < a < b ). (a) Describe how the conchoid x = cot t + 4 cos t , y = 1 + 4 sin t is generated as t varies over the interval 0 < t < 2 π . (b) Find the horizontal asymptote of the conchoid given in part (a). (c) For what values of t does the conchoid in part (a) have a horizontal tangent line? A vertical tangent line? (d) Find a polar equation r = f θ for the conchoid in part (a), and then find polar equations for the tangent lines to the conchoid at the pole.
A parametric curve of the form x = a cot t + b cos t , y = a + b sin t 0 < t < 2 π is called a conchoid of Nicomedes (see the accompanying figure for the case 0 < a < b ). (a) Describe how the conchoid x = cot t + 4 cos t , y = 1 + 4 sin t is generated as t varies over the interval 0 < t < 2 π . (b) Find the horizontal asymptote of the conchoid given in part (a). (c) For what values of t does the conchoid in part (a) have a horizontal tangent line? A vertical tangent line? (d) Find a polar equation r = f θ for the conchoid in part (a), and then find polar equations for the tangent lines to the conchoid at the pole.
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY