//// // , 



CXCRCIteS 



l it I,, *,,uatii, of the di.ii.-ur of the hyper boU 



> ton bisect* the chords jr = 3 x + A. 



1 also the conjugate diameter. 



2 I 1 1* hyperbola <>f I x I diameter through the point 



(1. !>. snd its conjugate. 



the diameter of the hyperbola ^ - = 1 which is coo- 

 ;^te to the diameter x - 3 y = 0. 

 4 Find the equation of aehor.l of the hyperboU rjjr* - 9jr*s 108 



5. I.::..- from any |nnt of an equilateral hyperboU to the extremi- 

 \ tie* of a diameter make equal angle* with the asymptotes. 



6. Show that, in an equilateral hyperbola, conjugate diameters make 

 i equal angles with the asytujHote*. 



7 The difference of the square* of two conjugate semi-diameters is 

 is equal to the difference of the squares of the semi-axes. 



T 



. angle between two conjugate diameters is sin l ~. 



I '/ 



9. The polar of one end of a diameter of an hyperbola, with reference 

 10 conjugate hyperbola, is the tangent at the other end of the 



10. Tangents at the ends of a pair of conjugate diameters intersect 



on an .i>\ inj.t. -t,-. 



173. Supplemental chords. As previously defined, chord* of a curve 

 are supplemental when drawn from any point of the curve to the ex* 

 totalities of a diam>tr. If. in ih- an.ilvti.- work of Art. 157. fr* is 

 replaced by t m and IN' an* the slopes of two supplemental 



chorda of the hyperbola, 1 1 natiufy the relation 



< 



Hut this is (aftr ) the rendition that exists between the 



lopes of tvpplemfntal rAortft r 



fartiUtl to a pair f' conjugate dittm- 



tli.- equilateral hyperbola, if. when a = &, thU relation ha* !>> 

 specUl value sW.l, 



