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?

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