UNSW MathSoc Championship Q9

Given that $(x,y)$ lies on the unit circle $x^2+y^2=1$ in a Cartesian plane, find the minimum possible value of $10x^2 + 28xy + 20y^2$ .

If this minimum value can be written in the form $a-\sqrt{b}$ , where $a$ and $b$ are positive integers, find $a+b$ .