Another word problem

[Guest]

A point P is moving in the plane so that its coordinates after t seconds are (4cos 2t, 7sin 2t), measured in feet.
a) Show that P is following an elliptical path. Hint: Show that (x/4)^2+(y/7)^2=1, which is the equation of an ellipse.
b)Obtain an expression for L, the distance of P from the origin at time t.
c) How fast is the distance between P and the origin changing when t= pi/8? You will need the fact that Du(sqrt U)=1/(2 sqrt U)

 

[Unco]

For (a), t can be eliminated by solving for cos(2t) and sin(2t) (eg. x = 4cos(2t) --> cos(2t) = ?), squaring and adding the two equations.

I think (b) and (c) are ok; you need to be more specific as to where you're having trouble.