

VCTIOA - 



I'M 



the hyperbola differ! from the ellipse only in th* 

 sign of 1 *, which is + in the ellip^- and in the hyper- 

 the standard equal lie hyperbola can be derived 



l\ the meth 1 it will IN- funnd t 



u*e of axes and notation a* there given, tin- n su, 

 . of that artirle apply equal: 



rbola. If now, since 1 ** is negat titiitmn 



P*=a\<*-\) is made, equation (6) (p. 1*1 > will become 







n- 



rimplest equation of tin- hyperbola. I 



'pt.itmn will be obtain- ! i.\ a different method. 



lia The first standard form of the equation of the hyper- 

 bola. Li-t /' !> the focus, 



\, and | 



ecwi nf tlu curve. 



Take D'D us the //-axis, with 

 the perjieiidii-ular ofi'X UJHUJ 

 it, through tin- i- aa, as the 

 *-axis. Let *2p denote tht 

 given distance OF* and let 



/* = (*, y) 



beany point <f the 1.-. u>. \\nli .... i linatea LP and MP. 



/'/' I.I'. [geometric equation] 



hut / /' = T/(*-*V + A and 



,0, . (1) 



h is the equation of the hy|>erbola referred t- 

 directrix and principal axis as coordinate axes (cf. Art. 



