NOTE ON THE INTERSECTION OF TWO CURVES. 



357" 



points on one branch r is positive, and for all on the other r is 

 negative. Call these I-\- and / — . I-\- is the branch nearer to the 

 common focus. Similarly call the branches of the second conic 

 // -f- and // — . The solutions of equation (A), taken between 

 o° and 360°, give the intersections of / -(- with // -(-. ^i^d those 

 of / — with // — , while the solutions of equation ( B), also taken 

 between 0° and 360°, give the intersections of / -j- with // — ,, 

 and those of / — with // -j-- 



I 

 In Figure i two hyperbolas are drawn, — rz: i -(- ^3 cos 0,. 



2r 



I 



— =1-1-2 sin (), intersecting in four points. Equation ( A) 



gives an intersection of / -j- with // -|- and an intersection of / — 

 with // — , the chord joining these being shown by a dotted line. 

 and equation (B) gives an intersection of / + with // — and 

 an intersection of / — with // -]-. these again being joined by a 

 dotted line. 



