S-79.] l.g 1:7 



EXERCISES 



1 thecentrr the radiu< 



2. the center < radiiu |; 



3. tbecetitrr theradituS; 



4. tl..- . . ut.-r (ii, 0), the radii* 5; 



5. the center (-4,0), th nuliu 



mro circlet related for which A and IT are the amroe, while r la 

 -nl for each? for which A and r are the same, while * differ, for 



7 \\ v : mi does the equation of the circle aatome when the center 

 U on tho iHUcis and the origin on tl rence? when the circle 



touches each axis and haa ite center in quadrant II ? 



79. In rectangular coordinates every equation of the form 



OP*+ y* + 2f;-r + 2Fy + C = represents a circle. The equa- 



des already obtained (equations [31] and 



[ : J ], aa well as the answers to examples 1 to 5 and 7) are all 



, f i triu 



=0 ; . . . (1) 



11 n< \\ l>e shown that, for all values of (7, F, and C, 

 fur \\lii.-h the locus of equation (1) is real, this equation 

 resents a circle. 



'I prove this it is only necessary to complete the square 

 in the x-terms anl in the y-terms, by adding (7 s 4- F 1 to each 

 iiher of equation (1), and then transpose Cto the secoml 

 member. Kquation (1) may then he written in the form 



(x 4- G? +(y + JF) 1 = <?* 4- F* - 



*- CO 1 . . (2) 



which is ( , f. r.ju.ition [31]) the equation of a ir.-le whose 

 center is the point ( #, /" V and whose radius is 





