Analytic Geometry!

1. -4/3, I just graphed it in desmos and fiddled with some stuff.

2. So the distance of the Center, (x,y), to B and A are the same.

We know that y is 5 from tangent rules.

(x,5)

The distance from (x,5) to (9,0) is x, since to B is also x

$\sqrt{(9-x)^2+25}=x$

$(9-x)^2+25=x^2$

$x^2-18x+106=x^2$

$x = \frac{53}{9}$

$(53/9,5)$