Give an equation to describe the locus of points P(x,y) where the distance of P from point A(4,1) is twice the distance of P from the line y=2?

Give an equation to describe the locus of points P(x,y) where the distance of P from point A(4,1) is twice the distance of P from the line y=2?

1 Answer
May 2, 2017

3y^2-x^2-14y+8x-1=0

Explanation:

Calling p_0=(4,1) and p = (x,y) we need

norm(p-p_0)=2abs(y-2) or

sqrt((x-x_0)^2+(y-y_0)^2)=2abs(y-2) or

(x-4)^2+(y-1)^2=4(y-2)^2

Simplifying

3y^2-x^2-14y+8x-1=0

The locus presents two leafs given by

y = 1/3 (7 pm sqrt[52 - 24 x + 3 x^2])

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