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)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.