I-J 1C : ; Kg -"7 



IK. The above rwmlu hare not all been hown, bat art easily 

 deduced from the work already given. Thua the loooa of equation 



% ift ima. -at, by equation (), Art. 



henoe the teat 1 (2), given above. And ao for 



the other tetta, which the student ahould verify. The angle $ which 

 ..iw axe* make with the old, respectively, U choeen ai in Art 

 taken alway* positive and not greater than I9tf. 



183. The equation of a conic through given points. The 

 general cquu-. i .-..in-- umy bo written 



// y + ^ + i'oV + iJJV+ff- ' . <1, 

 and contain* five parameter*, the five ratios between 

 coefficients A, IT, B, 0, t\ C. Since five equations, or < 

 us, will determine those parameters, in general five 

 t* will .Inn-mine a conic. That is, in general, a conie 

 may be made to past through jive, and only jfo*, ffJ9en 

 point*. 



. however, the conic is to be a parabola, one equation is 



H* AB = 0, hence only four additional 

 *iis are needed. In general, a parabola may be made to 

 pa** through four pointy only. 



\ Mas two nmditinns trivni, \i/. ^4. = B, H ** 0; 



then? fore, in general, a circle may be made to pat* through 



thr,-, i.'.i'n'*. ..,<!,/. 



\ lines has one condition A 



. in general, a pair of $trai>/ht line* may be made 

 ' * rough four point * > 



t. U fdlliiwi-d in ohtaining the equ.it; 

 tlu* n ,piin .I cnnii- has been used in Art. 80, and may be 

 .itr.l for finding tin- iMjuati.m <f the parabola through 



. 



7\ /' PgSOvJf,). and /' 



11 must l>c of tlu- I'.TIII ( 



