9/15/2014 Find the locus of points that is twice the distance from (-1, 2) than (3, 4). Identify the figure so formed.


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9/15/2014 Solution.
If the point is (x, y), then using the distance formula:
√[(x + 1)2 + (y – 2)2] = 2√[(x – 3)2 + (y – 4)2].
Squaring both sides and expanding:
[(x + 1)2 + (y – 2)2] = 4[(x – 3)2 + (y – 4)2]

x2 + 2x + 1 + y2 – 4y + 4 = 4x2 – 24x + 36 + 4y2 – 32y + 64

3x2 – 26x + 3y2 – 28y + 95 = 0 which is an ellipse.