ANALYTIC OEOMEIHY \\. 



6 For what points of an hyperbola are the subtenant anl 

 nonnal equal V 



7 (,i\.n tli.- hyperbola 9 y* - 4 ar* = 30, find the focal radii <>t th<> 

 point whose ordinal' <l abscissa posit iv. 



8. A tangent which is parallel to tin- HIM- .">./ I// + 7 = <>. i- drawn 

 to the hyperbola z f y*= 0; what is the subnormal for the point of u- 

 tact? 



9. What tangent to the hyperbola y -$=1 hasitsy-interc<>i 



10. Find, by equation [67], the two tangents to the hyperbola 

 4x* - 2y a = which are drawn through the point (:l. 



11. Find the polars of the vertices of an hyperbola with respect to its 

 conjugate hyperbola. 



12. Prove that if the crack of a rifle and the thud of the ball on the 

 target are heard at the same instant, the locus of the hearer is an 

 hyperbola. 



13. An ellipse and hyperbola have the same axes. Show that tin- 

 polar of any point on either curve is a tangent to the other. 



14. Find the equation of an hyperbola whose vertex bisects th 

 tance from the focus to the center. 



15. If e and e' are the eccentricities of an hyperbola and its conjugate, 

 then 



e* + e'* = e*e'*. 



16. If e and d are the eccentricities of two conjugate hyperbolas, 

 then 



ae = be'. 



17. Find the eccentricity and latus rectum of the hyperl>ola 



18. Find the tangents to the hyperbola 3jr- 16y a = 14 1. 

 with the tangent at the vertex, form a circumscribed equilateral ti 

 Find the area of the triangle. 



19. Find the lengths of the tangent, normal, subtangent, and sub- 

 normal for the point (3, 2) of the hyperbola z 2 - 2 y 2 = 1. 



165. Asymptotes. If a tangent to an infinite branch <>f 

 curve approaches more and more closely to a fixed straight 

 line as a limiting position, when the point of contact mov< 

 further and further away on the curve and becomes in tin itch 



