Find minimum value $E(x, y) = x^2 + y^2 -6x -10y$, where $x^2 + y^2 - 2y \le 0$ I am given the expression:
$$E(x, y) = x^2 + y^2 -6x -10y$$
And I have to find the minimum value of $E(x, y)$ for $(x, y) \in D$ where:
$$D = \{ (x,y) \in \mathbb{R}^2 \hspace{0.25cm} | \hspace{0.25cm} x^2 + y^2 -2y \le 0 \}$$
Doing the following:
$$\hspace{5.8cm} x^2+y^2-2y \le 0 \hspace{5cm} |+1$$
$$x^2+(y-1)^2 \le 1$$
So I have to find the minimum value of $E(x,y)$ where $(x, y)$ is from the circle $x^2 + (y-1)^2 \le 1$.
I don't see how I should approach this.

Note that $E(r) = r^2-34$, where $r$, given by the circle 
$r^2= (x-3)^2 + (y-5)^2$, is its radius and the circle $x^2+(y-1)^2=1$ has radius 1.
So, $E(r)$ is minimum if $r$ is the smallest, which is the case when the two circles just touch, i.e. the sum of their radii is equal to the distance of their centers, $r+1=\sqrt{3^2+4^2}=5$. Thus, the minimum $E$ is $(5-1)^2-34$.
