1. The problem statement, all variables and given/known data A particle is moving along the ellipse x2/16 + y2/4 = 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? 2. Relevant equations x2/16 + y2/4 = 1 x = 4cost y = 2sint dx/dt dy/dt 3. 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 x2/16 + y2/4 = 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 doesnt play any effect in finding dy/dx. Thank you.