SOLUTION: Hi Totally Bewildered, Please Help? The path of a point is given parametrically by x = a cos t, y = b sin t. Show that the point travels around the ellipse x^2/a^2 +y^2/b^2

Algebra.Com
Question 375015: Hi Totally Bewildered, Please Help?

The path of a point is given parametrically by x = a cos t, y = b sin t. Show that the point travels
around the ellipse
x^2/a^2 +y^2/b^2 = 1
Express dy=dx in terms of t. Suppose that t represents time. Express the speed as a function of t.
ii) A closed hollow vessel is in the form of a right-circular cone, together with its base, and is made of sheet
metal of negligible thickness.
Express the total surface area S in terms of the volume V and the semi-vertical angle 'theta' of the cone.
Show that for a given volume, the total area of the surface is a minimum if sin 'theta' = 1/3 . With this value of 'theta', find
the value of S if V = 8/3'pie' a^3 where a is a constant.
Sorry didnt know how to get symbols on this, so typed the names
Kind Regards
John
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Given



and



Square both parametric equations:



and



Recall the Pythagorean Identity



hence



Then substitute:



And finally:



John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism
RELATED QUESTIONS

Hi Please can somebody help with this problem i) The variables x and y are given (answered by Alan3354)
HiPlease can somebody help with this problem i) The variables x and y are given in terms... (answered by Fombitz)
Graph the line that is described parametrically by (x,y) = (2t, 5-t), then: (a)... (answered by greenestamps)
Given that cos t = 8/9 and that P(t) is a point in the fourth quadrant, find sin t.... (answered by ikleyn)
Given that cos t = − 2/5 and that P(t) is a point in the second quadrant, find sin... (answered by Alan3354)
Hi, I have 2 questions, Im so coonfused. 1) Let P be the point on the unit circle (answered by edjones)
The point P in the figure below has y-coordinate 12/13 . Find the following. (a) (answered by Edwin McCravy)
Please check my answers for questions related to Unit Circle A. Find the missing... (answered by stanbon,ewatrrr)