Asked 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.
a. Find the equation
b. tell which conic section the graph will be.
Answers
Answered by
Steve
let d1 = distance of (x,y) from (3,4)
d1^2 = (x-3)^2 + (y-4)^2
let d2 = distance from (-5,2)
d2^2 = (x+5)^2 + (y-2)^2
since d1 = 4*d2
d1^2 = 16*d2^2
(x-3)^2 + (y-4)^2 = 16[(x+5)^2 + (y-2)^2]
expand and collect terms to arrive at
(x+83/15)^2 + (y-28/15)^2 = 7234/15
Looks like a circle
d1^2 = (x-3)^2 + (y-4)^2
let d2 = distance from (-5,2)
d2^2 = (x+5)^2 + (y-2)^2
since d1 = 4*d2
d1^2 = 16*d2^2
(x-3)^2 + (y-4)^2 = 16[(x+5)^2 + (y-2)^2]
expand and collect terms to arrive at
(x+83/15)^2 + (y-28/15)^2 = 7234/15
Looks like a circle