Math/conics
posted by Mason .
For each point in a set of points, its distance from (3,4) is four times it's distance from (5,2)
a. Find the equation
b. tell which conic section the graph will be.

let d1 = distance of (x,y) from (3,4)
d1^2 = (x3)^2 + (y4)^2
let d2 = distance from (5,2)
d2^2 = (x+5)^2 + (y2)^2
since d1 = 4*d2
d1^2 = 16*d2^2
(x3)^2 + (y4)^2 = 16[(x+5)^2 + (y2)^2]
expand and collect terms to arrive at
(x+83/15)^2 + (y28/15)^2 = 7234/15
Looks like a circle