400 



23. If the bane (=2 a) coincides with th r-.ixis, it* middle point at th.- 

 origin, and if A- = the area of the triangle, then the locus of the vertex is 

 ay - k = 0. 



85. lOx = 7 (axes chosen as in Ex. 23). 



86. (a) x=0, y=0, x-y=0; (ft) 7x+y=0, 2x-y=0; (>) x=0, y=0. 



87. c = -3. 81. x-4y + 8 = 0; 9x-4y = 2l. 



88. 25x-14y = 120. 88. x = 0. 84. x 2 - y 2 = 0. 

 86. 3y-26x = 3, 122y-37x = 10, 31x + 78y = 190. 



36. (a) 



Pages 125. 126 Art. 71. 

 1. 3* - 2 y = 0. 8. jr + y = 31. 8. 2 y - 4 a* + 1 = 0. 4. y = 



Page 127. Art. 72. 



1. x -I- y = 16. 2. xy = - 8. 8. V2 y + 1 = 0. 



4. 



Page 128. Art. 73. 



1. 4 a* = '->.-.. 2. x = x'--, y = 



3. y = 0, x = 0, and 



Page 129. Art. 74. 

 = 6; 12x a - 18xy + 9y = 6. 



Page 131. Art. 76. 



1. p = a. 2. p sin & cot 4- 2 a = 0. 8. cos 25 = 1. 



4. tan = tan a. 5. p(cos 4- V3 sin 0) = 2. 6. />*CO820 = 4. 



7. x + y a = a 2 . 8. x 2 - y 2 = a 2 . 9. xy = 6. 



10 (x 2 + y 2 ) 2 = 2 axy. 11. x 2 + y 2 = te. 12. lly = 2x. 

 18. y' + 4*x = 4* 2 . 



Pages 132-134. Examples on Chapter VI. 



= 0. 2 >/6 2 + 6 = 0. 8. yi-xy = Q. 



4. y*+xy + 6>/2y = 0. 6. ('2,2). 7. x + y = 0, 2* - 3y = 0. 



8. y = 0. 9. tanf = f. 11. tan tf = -^; tan ^ = - 



. 1 



