Question

give a parametric representation of the ellipse whose equation is given with the orientation being clockwise. 100x^2+25y^2-2500=0

Answer 1

Rearranging that equation you can get: \[(\frac{ x }{ 5 })^2+(\frac{ y }{ 10 })^2=1\] From this, notice that if we let \[x/5 = \pm \cos(t) => x= \pm 5\cos(t)\] and similarly, \[y/10 = \pm \sin(t) => y= \pm 10\sin(t)\] is a solution to the same ellipse
to get a clockwise rotation we need to determine the correct signs. Since, t is going clockwise as t increases we want x and y to decrease, since cosine starts as a decreasing function (starting at t=0) we will leave x as the positive solution. However, change y to the negative solution.
Therefore, \[x=5\cos(t), y=-10\sin(t)\]

Answer 2

ty so much