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EXERCISES 



Tinine for each of UM following hyperbola* UM eauCer, emi-aon, 

 c<, and laluft rectum : 

 .H_8y + (Hx - .*Jy + 10 = 0j 



x + Of + Sf* * -I- 7. 

 4 Reduce UM equation* of eiercim 1, 2, 8, to the standard form 



- ^ 1. flkatoh each curve. 

 fr* 



120. Summary. In the preceding articles it has been 

 shown that the special equation of the second degree, 



\,3 + By* + -2 6 /y+tf-O, 



always represents a conic section, whose axes are parallel to 

 the coordinate axes. There are three cases, corresponding 

 > three species of coni* . 



( 1 ) The parabola: cither A or B is zero. In exceptional 

 oases this curve degenerates into a pair of real or imaginary 

 parallel straight lines, and these may coincide. [Art. 107] 

 . Hie ellipse : neither A nor B is zero, anil they have 

 likr signs. In exceptional cases this curve degenerates into 

 a circle, a j>oint, or an imaginary locus. [ Art. 



(8) The hyperbola: neither A nor B is zero, ami t 

 have unlike signs. In exceptional cases this curvj (leg* ; 

 ties into a pair of real intersecting lines. [ A it . 119] 



The ellipse and hyperbola have centers, ami th.-r.-t..re are 

 called central conies, while the parabola is said to be non- 

 central; although it is at times more convenient to OOM 



the latter curve has a center at infinity, <>n the )>nm-i- 

 pal n\ Appendix, Note 



The equation for each conic has two standard forms, which 

 State a characteristic geometri* : he curv. 



whirh all other equations rej.re>ent in^ that >j.e. ir Otfl ii- 



