Geometry
# Conic Sections

What is the number of intersections between $y=4$ and $x^2+y^2=9$?

Point $O$ is the center of the ellipse with major axis $AB$ & minor axis $CD$ Point F is one of the focus of this ellipse.

If $OF=6$, and the diameter of inscribed circle of triangle $\triangle{OCF}$ is $2$, then find $(AB)\cdot (CD)$

There are four lines that are tangent to both circles

${ x }^{ 2 }+{ y }^{ 2 }=1 \quad \text{ and } \quad ({ x }-6)^{ 2 }+{ y }^{ 2 }=4.$

What is the sum of the slopes of these four lines?