

< II \M I.K XI 

 The Hyperbola, g-g. I 



160. Review. The definition of the hyperbola given in 

 < i \ III led at once to two standard forms for its equa- 

 f. Arts. 116, 118): 



5-*-. 



when the axes of the curve are <->i undent with the coordi- 

 nate axes ; ami 



(*-*) (.V-*^! 

 * P 



when the axes of the curve are parallel to the coordinate 

 axes, and its center is tin- point (&, k). 



A In iff discussion of the first standard form ^ =! 



a 1 A* 

 bowed th.it tin- curve has its eccriitricit\ ^ivm i>\ th<> rela- 



^^^(^-l), i.e., by = ^^; its foci are the 

 " >, and its directrices the lines a?j 

 110). These results are entirely analogous to 

 corresponding ones for the ellipse, if it he remembered that 



1 * is positive for tin- ellipse, while <* 1 is positive for 

 . perbola. 



-iinil.irity <>f the equations <>f the hyperbola and the 

 ** leads to various correspiileiu'es in the an :p- 



erties of the curves. For example, the equation 





?. 



IN 



