ntr iD'pgRno 

 i//' .-.|ual to AM/ .(v / b a point of the hyperbola. 



.11 lh- ri-hl IIIUIIK. 



'.' ;, "M :. 



Jf'ftsOfttau*. - Uft^frtaiieV 



U 



ami P b a point on the hyperbola.* 



The eccentric angle for any giv-n ]*...,-. /. of an hyperbola b eatily 

 obtained. Draw the ordinate .I//', >. , foot, AT, draw a tangent 



MQ to the r-uux iliary circle ; then the angle MOQ to the eccentric angle 



(/?) The equation of the hypcrlx>ia n-ferred to iU acymplotea, viz. 

 ry = r, b aatbfled by the oodrdinaiea * = rf, y = f . whatever the value* 



of/. ThMiM..f t!. .'lependent variable fbaometiineaconrenient 



in dealing with pointa on the hyperbola.* 



h EXAMPLES ON CHAPTER XI 



t) ..... : an hyperbola whoee transTerae azb b 8, 



the conjugate azb one half the dbtance between the i 

 1 the equa it diameter of the hyperbola 16x-0^= 144 



eh paaaea through the point (5, V); abo find the eoordinalM of the 

 eitremitiea of the conjugate diameter. 



3. Assume the equation of the hyperbola, and show that the difference 

 of the focal dbtanoea b constant. 



1 the locus of the vertex of a triangle < : the 



of the two other sides b a constant, and equal t . 



5. Kind the locus of the vertex of a triangle of given base, if the 



of the tangents of the base angles b const* 



6. Find an expression for the angle between any pair of conjugate 

 diameters of an hyperbola. 



7. Show that two concentric rectangular hyperbola*, whose 

 meet at an angle of 45, cut each other orthogonally. 



The forms of thb article arc useful in the differential calculus. 



GKUM. 10 



