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Homework Statement
Find the points on the ellipse 4x2+y2=4 that are furthest from the point (1,0) on the ellipse.
Homework Equations
Ellipse: y=±√(4-4x2)
Distance Formula: d=√[(x2-x1)2+(y2-y1)2]
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.
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