There's a straight line going from B to C in the first quadrant of x,y coordinate system.
B is $(0,s)$, C is $(t,0)$
Let A $(3,3)$ be a point on the line going from A to B.
Find the equation of the line so the distance between B and C will be minimal.
Well, I've started by finding points that their squared distance is minimal \ maximal (Helps me getting rid of un-needed roots) so the distance between B and C is $f(x)=x^2+y^2$.
Now i wanna find a restrict equation and use Lagrange multipliers. But i can't find a proper one.
Guidelines please?
The distance between $B$ and $C$ is $\sqrt{s^2 + t^2}$ so you need to minimize $f(s,t) = s^2 + t^2$. The fact that $A$ lies on the segment connecting $B$ and $C$ gives you a constraint: compare slopes to get $\dfrac{3-s}{3} = \dfrac{3}{3-t}$, which is equivalent to $st - 3s - 3t = 0$. Let $g(s,t) = st - 3s - 3t$ and minimize $f(s,t)$ on the level set $g(s,t) = 0$.