278 ANALYTIC GEo.M /://;>' [<'.. \ I. 



7 \Vrita the equation of the hyperbola conjugate to thai . i \.\ <> 



8. Kind the equations of the asymptotes of the hyperbola 



f-S*sBjr* + f + 6i 

 also find the equation of the conjugate hyperbola. 



9. Find the equation of the asymptotes of the hyperbola 



r 1 1 y* - x + 21 y = 0. 



10. Kind the equation of the hyperbola conjugate to 



* - 16 y + 30 x + 160y = 508. 



11. Prove that a perpendicular from the focus to an asymptote of an 

 hyperbola is equal to the semi-con jug; r 



12. The asymptotes meet the directrices of the /--hyperbola on the 

 z-auxiliary circle, and of the conjugate hyperbola on the y-auxiliary circle.* 



13. The circle described about a focus, with a radius equal to half the 

 conjugate axis, will pass through the intersections of the asymptotes 

 and a directrix. 



14. The line from the center C to the focus F of an hyperbola is the 

 diameter of a circle that cuts an asymptote at P; show that the chords 

 CP and FP are equal, respectively, to the semi-transverse and semi- 

 conjugate axes. 



168. The hyperbola referred to its asymptotes. If the 

 asymptotes of an hyperbola are chosen as the coordinate 

 axes, their equations \\ill be # = and y = 0, respectively; 

 or, combined in one equation, 



xy = 0. . . . (1) 



By the reasoning of Art. 166, it follows that the equation 

 of the hyperbola, which differs from that of its asymptotes 

 by a constant, is 



wherein the value of the constant k is to be determined l>y 

 an additional assigned condition concerning the curve ; <?.</., 

 that it shall pass through a given point. 



