1. The problem statement, all variables and given/known data Find the points on the ellipse 4x2+y2=4 that are furthest from the point (1,0) on the ellipse. 2. Relevant equations Ellipse: y=±√(4-4x2) Distance Formula: d=√[(x2-x1)2+(y2-y1)2] 3. The attempt at a solution The distance from (1,0) for any point on the ellipse should be d=√[(x-1)2+(±√(4-4x2)2]. That simplifies to d=√[(x-1)2+4-4x2]. The ± in front of √(4-4x2) just turns positive because the final value is squared anyways, right? However, when I graph the distance formula it doesn't match up with my ellipse. According to my solution manual the maximum distance occurs at x=-1/3, but my distance formula graph just keeps increasing. The manual squares d to give s=d2 and then graphs s, which does give a maximum value for s at x=-1/3, but I don't understand why they do this and how it works. Edit: Added negative sign to x=-1/3.