NYJC/2021/JC2/Prelim/P1/Q04

A curve $C$ has cartesian equation

$y=\frac{x}{1-x}, 0 \leq x<1 .$

(i) The distance between a general point $(x, y)$ on $C$ and the fixed point $(1,0)$ is denoted by $s$. Show that $s^2=(x-1)^2+y^2$

[1]

(ii) Use differentiation to determine the coordinates of the point on $C$ which has the minimum distance from the point $(1,0)$, giving both coordinates correct to 4 decimal places.

[5] [You need not prove that this distance is a minimum]
(iii) Find this minimum distance.

[1]