//// // 



22. Show that, in an equilateral hyperbola, two diameters at right 

 angles to each other are equal Show alo thai thu follow* fn. 



23 A variable circle is always tangent to Mr ftxed circlm; 

 prov that the loom of iu center if either an hyperbola or an ellipse. 



24 !:-...! iho coiniuuu tangenta to the hyperbola ;- 1 d iu 

 miiUircIo x + j* a 06, 



25. IM the hyperbola 25 x* - 18 J* 4<X)^ find the con jugate diameters 

 thai eut each other at an angle of 45. 



26. The latus rectum of an hyperbola U a third proportional to the 

 two axes. 



27. The polara of any point (A, Jr) with respect to conjugate hyperbolae 



28. The sum of the eccentric angles of the extren vo conju- 

 gate diameters of an hyperbola is equal to 00; i.r. f ^ ^ ^' = 00. 



29. Find the equation of a line through the focus of an hyperbola 

 an<l the focus of iu conjugate, and find the pole of that line. 



30. Fin-1 the asymptotes of the hyperbola xy - 3x - 2f = 0. What 

 la the equation of the conjugate hyperbola? 



31. Show that the y-axis is an asymptote of the hyperbola 



v + 3x* + 4x = 9. 



What is the equation of the other asymptote? Of th conjugate 

 hyperbola? 



32. If two tangents are drawn from an external point to an hyperbola, 

 they will touch the same or opposite branches of the curve according as 

 the given point lies between or outaide of the asymptotes. 



