.\\.\I.YIK QEOMEinY \II.183. 



therefore, Ar* + 2 ^jy j + By f + 2 0^ + 2 .Fy, + C Y = 0, 



-' + 2Ux4i+By* + 2Gxi + 2Fi/i+ (7=0 



also. JP 



Tin* required ratios between the coefficients of equation 

 may be found from these equations. 



EXAMPLES ON CHAPTER XII 



Without transforming the equations to other axes, find the center 

 or the vertex, the axes, and the nature of the following conies: 



2. (jr-y) + 2x-y=l; 



3. 3* 2 +2y>-2;r + y-l=0; 



4 :}* - 8 xy - 3y + x + 17 y - 10 = 0; 



5. 4a: 2 -4;ry + y* + 4<u:-2fly = 0; 



6. 5x a + 2ry -f 5y 2 = 0; 



7. 3x 2 + 3y 2 +llx-5y + 7 = 0; 



8. x 2 + 2*y-y 2 + 8;r + 4y-8 = 0; 



9. y2_ a #_ 6j: 2 + y _3 a . = o ; 

 10. y2-x-5ar + 5 = 0. 



Trace the following conies : 



12. I** -f 0^ + 



13. 3r2-3y2 + 



14. (x-y)(.r-y-C)+9=0. 



15. What conic is determined by the points (0, 3), (1, 0), (2, 1), 

 ( 1.-3), and (3, -3)? 



16. Find the equation of the parabola through the points (3, 2) f 

 <M). (-6, 8), and (-2, $). 



17 Find tlio -.j nation of the conic through the points (9, 2), (J, 3), 

 (-'. I)- 



