Turn BSC and the O and O' about the axis of the cone. BS and CS will generate the surfaces of the two nappes of a right circular cone; and the O, O' will generate spheres which touch the cone in the plane in the points F, F'. DKH, D'K'H', and the secant Let P be any point on the curve. Draw PF and PF'; and draw PS, which touches the DKH, D'K'H', at the points K, K'. Now PF and PK are tangents to the sphere O from the point P. Therefore, the curve is an hyperbola with the points F and F' for foci. § 945 Q. E. D. r = apothem of regular polygon. a, b, c = sides of triangle. s = (a + b + c). p = perpendicular of triangle. m, n = segments of third side of triangle adjacent to sides b and a, respectively. |