ran LA 



tin- line through /' { ati'l /', ii 



'i-fKr?*'-' 



*i ''i 



1 must have a value determined by equation* 

 f \ 



<:;>, 



quutinn MTiint liiu- /' 



y-yi--- -^). . . (4) 



It" now the jM.int /*, becomes coim-iiU-nt \\itli P v eqiui 



r - ft - - 



^i 



\vhirli may be reduced by equation < J> to 



y,r -f r t y 2 c 1 , 



h is t)ie iv<juir.-l c<|tiati.>n of the tangent at the JM unt 

 /' nrve. 



170. Geometric properties of the hyperbola. Kqiiatinn [ 

 H Uie following intrinsir \- f.r tin- liv]Hrliola, 



U'inij any j-oint mi tlir mrve (l'i-. 11 



\ I//' 



that U. for every pot hyyfrLnLi.four time* thf product 



^9 from the a*ym}>tott*. measured parallel to tke 

 *ymptotf* re*pf, | .-^mil to the tquare of the </itfmM9 



front the centtr to the focut ; and i* therefore constant. 



