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## Homework Statement

A particle is moving along the ellipse x

^{2}/16 + y

^{2}/4 = 1. At each time t its x and y coordinates are given by x = 4cost, y = 2sint. At what rate is the particle's distance from the origin changing at time t? At what rate is the distance from the origin changing when t = pi/4?

## Homework Equations

x

^{2}/16 + y

^{2}/4 = 1

x = 4cost

y = 2sint

dx/dt

dy/dt

## The Attempt at a Solution

I am fairly sure i can do this question, the only problem is that i am not so sure what it is asking for. I'm assuming that i am to find dy/dx.

dy/dx = (dy/dt)(dt/dx)

dy/dt = 2cost

dx/dt = -4sint

x

^{2}/16 + y

^{2}/4 = 1

2x(dx/dt) (1/16) + 2y(dy/dt)(1/4) = 0

(x/8) (-4sint) + (y/2)(2cost) = 0

(-xsint)/2 + ycost = 0

At t = pi/4

2ycos(pi/4) = xsin(pi/4)

2y(1/√2) = x(1/√2)

x = 2y

dy/dx = (dy/dt) (dt/dx)

= (2cost)(-1/4sint)

= (-1/2) (cost/sint)

= (-1/2)(cott)

at t = pi/4

dy/dx = (-1/2)(1/1)

= -1/2

Does this mean that the answer is -1/2 because then I'm not sure why they gave us the equation for the ellipse because it doesn't play any effect in finding dy/dx. Thank you.

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