163-UH.] ////: //>// 







It follows at once that tho l.vjM-rlM.la (2), conjugate to 



, x ; . h* 



~r~ f 



'* (0, 5**), and f..r direct ncr.s tin* lines 



Two conjugate hyperbolas have a common center, and 



B all .it tin- common distance Vo 1 + > 



cent* iln foci all lie on a circle about the cei 



ug for nuliuH the semi-diagonal OS of the rectangle 

 'inn ion axes, and whose sides are tangent to the 

 - s at thi-ir vertices. Moreover, whni the curves are 

 construct.-.! it will U found that they do not intrr-i-rt. hut 

 are separated by the extended diagonals OS and OK of 



imscrihed rectangle, \\ hi.-h they approach from opposite 

 aides. These diagonals are examples of a class of lines of 

 great interest in analytic theory ; they are called atymptoUt 



EXERCISES 



1. Construct an hyperbola, given the <li*Unr* hetwr> i a 

 8 cm. and r = 2. 



2. Construct an hyperbola, given the distance from directrix to focus 



a.H j i-iii. ! iv MM h hyperbolas are posdbleT 



3 u :t4. the equation of an hyperbola conjugate to the hyperbola 

 x* - 16 f = 144, and find its axe*, foci, and latus rectum. Sketch the 



4 \\Mte the equations of the tangent and normal to the hyperbola 

 16 x* - 9 y* = 112 at th. 4), and find the tubtangent and sub- 

 normal. 



5 W - t i equations of the polar* of the point (I. I) with 

 to the hyperbola Ox* - 16y = 144 and iu conjugate, respectively. 



