1. The eccentricity of a rectangular hyperbola is \ sqrt { 2 }. 2. A circumconic passing through the orthocenter of a triangle is a rectangular hyperbola . 3. The graph of two variables varying inversely on the Cartesian coordinate plane is a rectangular hyperbola . 4. Dionysodorus solved the cubic by means of the intersection of a rectangular hyperbola and a parabola. 5. In the case of a rectangular hyperbola , its conjugate is the reflection across an asymptote. 6. The rectangular hyperbola xy = 1 can be used to gauge velocities ( in the first quadrant ). 7. These three hyperbolas are all rectangular hyperbolas where the asymptotes are parallel to the x and y axes. 8. Dionysodorus is remembered for solving the cubic equation by means of the intersection of a rectangular hyperbola and a parabola. 9. Note that the locus of the perspectors of this family of rectangular hyperbolas will always lie on the four orthic axes. 10. The unit hyperbola is a special case of the rectangular hyperbola , with a particular eccentricity equals \ sqrt { 2 }. 
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