

fo.V.s 



181 



9*o axea are parallel t<> tin- < axes. A- 



umurical caae will iir>t U- ,-\,umn.-.l. ami then 

 general equation taken up in a similar maim 



:XAMI-I.:. (iivfli the equation I r + y* - 16* + 1H y - 11 - 0. to 

 w that it represenU an ellipse, and to find its elements. 





v 



" 



quare for the ternia in r, and also for those in y, and transpocing, 



- 16x+ 16 

 4(r - 



lit equation is of the form [!:.]. and, therefore, its locus has the 

 property given in Art. IU. i ..I is an ellipse. Its center is 

 1 ) ; its major axis is parallel to the x-axU, of length 6 ; 

 .ixis is of length 4 ; the foci are the points 



F= (2 - Vk -1), F = (2 + v/5. 

 and the equations of the directrices are, respectively, 



o o 



* = 2 + -ir, *: ==. 



VS V5 



t|,,. mrtliM.l illusirat,Ml aUive, of oompl- 

 uares, the general equation (1) may be writ: 



