Math CentralQuandaries & Queries


Question from Ericka:

Find the locus of points three times as far from (0,4) as from (2,0)

Hi Ericka,

Suppose $(x, y)$ is a point on the locus then its distance from $(0 ,4)$ is

\[\sqrt{(x - 0)^2 + (y - 4)^2}.\]

What is its distance from $(2 ,0)?$ The distance from $(x ,y)$ to $(0, 4)$ is three times the distance from $(x ,y)$ to $(2, 0).$ This gives an equation in $x$ and $y.$ Simplify the equation.


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