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 ->  Quadratic Equations and Parabolas -> 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       Log On


   



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) About Me  (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

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