Question

consider the point (x,y) lying on the graph of y=(x+3)^1/2. let L be the distance between the points (x,y) and (4,0). write l as a function of y

Answer 1

$L=\sqrt{ (x-4)^2 + y^2 }$
and 
$y=\sqrt{x+3} \Rightarrow x = y^2-3$

$L=\sqrt{ (x-4)^2 + y^2 }=\sqrt{ (y^2 - 3-4)^2 + y^2 }=\sqrt{ (y^2-7)^2 + y^2 }$