284 AN M.) TET XL 



5. Express the angle between the asymptotes of an hyperbola in terms 

 of c; i.e., in terms of the eccentricity of tin- 



6. The segment of a tangent to an hyperhol.i int. rcepted by tin* 

 conjugate hyperbola is bisected at the point <>t >ntact. 



7. Show that the pole of any tangent to the rectangular hyperbola 

 ary = r-. \\ ith respect to the circle z* + y* = a*, lies on a concentric and 

 similarly placed rectangular hyperbola. 



8. Prove that the asymptotes of the hyperbola xy = hx + ky are 

 x = *, and y = h. 



9. Derive the equation of the tangent to the curve xy = hx -f ly at 

 the point P = (z lt y t ) on the curve. 



171. Diameters. A diameter has already been defined 

 (Art. 129) as the locus of the middle points of a system !' 

 parallel chords, and in Art. 152 the equation was derived 

 for a diameter of an ellipse. By the same method, if a sys- 

 tem of parallel chords of the hyperbola 



have the common slope m, the equation of the com^ponrUiiL: 

 diameter will be found to be 



This equation shows that every diameter of the hyperbole 

 passes through the center. 



(''inversely, it is true, as in the case of the ellipse, 

 every chord of the hyperliola through the center is a diam< 

 ter. That chord of the original set which passes tli 

 the center is the diameter conjugate to [71]; and its e<|ii 

 t i in is 



