Particle A starts at A(1,0) and moves in the first upper half of the elipse 4x^2 + y^2=4 at what point is the particle farthest from Starting point A , what is the maximum distance ?

Question

Particle A starts at A(1,0) and moves in the first upper half of the elipse 4x^2 + y^2=4  at what point is the particle farthest from Starting point A , what is the maximum distance ?

mww · Answer

This one is a tricky one. I recommend you write distance in terms of  a parameter, theta
using x = a cos (theta) and y = b sin (theta). Then differentiate distance wrt to theta and find what theta will give you the maximum distance.

irishboy123 · Answer

use the distance formula $s^2 = (x-1)^2 + y^2$  and replace $x^2$ with the $y^2$ using the equation of ellipse so that it becomes an expression in x only

then set $\dfrac{d (s^2)}{dx} = 0$