.' /:/./// I'M 



lie tilt* jiiiit i< ii < . , \vliicii m00w to6 OQFTO 



in ili< ; , yj) and P t a(x r y s ). Let 



^(j/, y 1 ), be til-- iin-Ml.- . . to thai 



(8) 



LTie coordinates of P l au-1 P s are found by solving 

 a* simultaneous equations, therefore the abscissa* 

 M.I Xg are the roots of the equation 



4 (a** 1 + $*)/* + 2aiur-HaM-aV = 0, . . . 



nates y l and y t are roots of tlu* ju.it i-n 

 (om4-^)y I -2^y-f*M--aVm-0. . 

 e, by Art. 1 1, ; iinutus of P* are 



Now, by varying the value of <% iMju.it i.-n (6) gives the 



li nates of the middle point for each >f tlu* lnnls of the 



n set. It is required to find tin* locus of P* for all 



values of <r, i.., to find an equation satisfi* and y*, 



