Question

What is the radius of a circle in which a 30° arc is 2 inches long?

Answer 1

Passing a plane through a double cone parallel to the axis of the cone produces a double curve called a hyperbola. Graphing the equation shown also produces a hyperbola. Moving the plane closer to or farther from the axis of the cone will change the size of the hyperbola but will not change the basic equation. The equation of a hyperbola is somewhat complicated because it depends on two lines that cross at a point midway between the hyperbola's two foci and extend outward an infinite distance, getting closer and closer to the hyperbola but never quite touching it. The distance from any point on either half of a hyperbola to the far focus minus the distance to the near focus is always the same for that hyperbola.