CONIC SECTIONS. OF THE HYPERBOLA. DEFINITION. 1. If B and C, are two fixed points, and a rule A B be made moveable about the point B, a string A DC being tied to the other end of the rule, and to the point C, and if the point A is moved round the centre B, towards E, the angle D of the string A D C, by keeping it always tight and close to the edge of the rule A B, will describe a curve DF HG, called an hyperbola. 2. If the end of the rule at B was made moveable about the point C, the string being tied from the end of the rule A, to B, and a curve being described after the same manner, is called an opposite hyperbola. 3. Foci are the two points B, and C, about which the rule and string revolves. 4. Transverse aris is the line I H, terminated by the two curves passing through the foci if continued. 5. Centre is the point M, in the middle of the transverse axis I H. 6. Conjugate axis is the line N O, passing through the centre M, and terminated by a circle from H, whose radius is M C, at N and O. 7. Diameter is any line V W, drawn through the centre M, and terminated by the opposite curves. 8. Conjugate diameter to another, is a line drawn through the centre, parallel to a tangent with either of the curves, at the extreme of the other diameter, terminated by the curves. 9. Abscissa is when any diameter is continued within the curve, terminated by a double ordinate and the curve, then the part within is called the abscissa. 10. Double ordinate is a line drawn through any diameter, parallel to its conjugate, and terminated by the curve. 11. Parameter, or latus rectum, is a line drawn through the focus, perpendicular to the transverse axis, and terminated by the curve. 12. Asymptotes are two right lines drawn from the centre M, and the points R S, which is parallel to the conjugate axis N O, and drawn through the end of the transverse axis IH; HR, and HS being equal to M N or M O, then MX, and M Y, are asymptotes. 13. Equilateral or right angled hyperbola is when its transverse and conjugate axes are equal. |