.4.1 ////: f/. /.//** Ml 



,ui'l tins equation r\|.ivHM-s the rtnidi: .: Una [62], 



li him the lope m', shall bisect tin- . i...i-l ;*j m 



expresses aim* the condition 



tin- hue [68] which luu* the slope m shall biiieet the 

 U uf Hlope m'. Hence each <f the linen [62] and [68] 

 l.isr.-tN the riiMi-.u p.u.iiiei i.. tl..- ..tii.-i. II. -n .. i' an 

 diameter biiect* the chord* parallel to a tecond, then aUo th* 

 ttcvnd diameter bitect* the chord* parallel to the firit. Such 

 diametera are callrl conjugate t<> carh \ 



\\ lin<- nf tin- srt >f jmniUfl chonhi in general cut* the 

 M in t\\ t JM. mts, ami tin- furtln-r tli- rli,.: 



tlu* center, the nearer these two points are to each 

 1 i.. their mi<l-i><int. In tin- limiting position, the 

 I becomes a tangent, with the two intersection \ 

 and thfir miil-pint coincident at the point of tangiMicy. 

 l e tangent at the end of a diameter i' parallel to 

 the conjugate diameter. This property, with that of Art. 152, 

 Mi^i-M.s .1 mrtho.l t'..r consinictini: conjm:.it ( - 'li.un'-t.-r^ : 

 first draw a tangent at an extremity of a given -li-u 



iicn ; ( line .Irawn parallel to this tangnit through 

 enter of the ellij.se is the required conjugate diani> 

 (See Fig. 111.) 



154. Given an extremity of a diameter, to find the extremity of its 

 conjugate diameter. 



0V .Vi) t* *n extremity of a given diarnet 11). Una 



P,=(-x,, -/,) will be the other extremity. Let 7 > 1 ' = (r l '. ..-, ) tad 

 JV = (-V- : y, ) - the extremitiea of theoonjugmte diameter. Let the 

 equation of the ellipse be 



then the equation of the given diameter Pf t b 



= ... (2) 



