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

**Scroll
down for the solution.**

**9/15/2014
**Solution.
If
the point is (x, y), then using the distance formula:

√[(x + 1)

Squaring both sides and expanding: [(x + 1)

→
x^{2}
+ 2x + 1 + y^{2
}–
4y + 4 = 4x^{2}
– 24x + 36 + 4y^{2}
– 32y + 64

→
3x^{2}
– 26x + 3y^{2}
– 28y + 95 = 0 which is an ellipse.