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?

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Answer 1 · 2017-05-02T10:22:41

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

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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