Find the points on the ellipse 4x2 + y2 4 that are farthest away from the point(-1, 0) Step 1 Let (x, y) be a point on the ellipse

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Find the points on the ellipse 4x2 + y2 4 that are farthest away from the point(-1, 0) Step 1 Let (x, y) be a point on the ellipse. We must maximize the distance between this point and the point (-1, 0), which is given by Step 2 Since the point (x, y) is on the ellipse 4x2 + y2 -4, then y2-4 - 4x2. We will optimize d by optimizing S = d2 . We have 1)2 + (4 - 4x2) Step 3 To optimize S, we solve 0 = S' = 2, thereby obtaining x-2/6 1/3 Step 4 Since S"-6 which is negative, then S has a maximum at x = .. There are two y. values for this x-value;