Question 19
Let $a,b,c,d$ be real numbers such that
$$\begin{cases}a^2+b^2+2a-4b+4=0,\\c^2+d^2-4c+4d+4=0.\end{cases}$$
Let $m$ and $M$ be the minimum and the maximum values of $(a-c)^2+(b-d)^2$, respectively. What is $m\times M$?
$$\begin{cases}a^2+b^2+2a-4b+4=0,\\c^2+d^2-4c+4d+4=0.\end{cases}$$
Let $m$ and $M$ be the minimum and the maximum values of $(a-c)^2+(b-d)^2$, respectively. What is $m\times M$?