Question 1132429


let point {{{P}}}({{{x}}},{{{y}}}) be on the locus, and {{{A}}}({{{1}}},{{{4}}}) given point

distance from {{{x}}} axis is equal to {{{y}}} coordinate,so 

so, given {{{AP=y}}}

=> {{{(AP)^2=y^2}}}

=> {{{y^2=(x-1)^2+(y-4)^2}}}

 {{{y^2=x^2-2x+1+y^2-8y+16}}}

{{{y^2-y^2+8y=x^2-2x+17}}}

{{{8y=x^2-2x+17}}}

{{{y=(1/8)x^2-(1/4)x+17/8}}}


{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(1,4,.12),locate(1,4,A(1,4)),
graph( 600, 600, -10, 10, -10, 10,(1/8)x^2-(1/4)x+17/8)) }}}