mi 



tf 



it will be shown that, in (artesian coordinate*, an equa- 

 find degree in two variable* always represent* a straight lint. 

 >n f*# tquatia* / = 4 x, to /</ i/J /oriu. ThU equation it 



attUfied bj each of the following pairt of values, found as in (3) abof: 

 , = 0, y, t. 



- 



-2^ approximately 



and for any negative value of x the corre- 

 ponding value of y U imaginary. 

 The oorratponding pointo are : 

 f>iB(0. 0), ^,8(1, 2), P,= r.i: 



: theae point* are found to lie on the curve an plotted in I .. 17. 



This curve U called a poroMa, and will be studied in a later chapter. 



The parabola is one of the curves obtained l-y th> intersection of a 



AT cone and a plane, (cf. App*-: D.) It will be shown 



in Chap. XII that in Cartesian coordinates, the locus of any alge- 



braic equation in two variables and 

 of the second degree is a "conic aec* 

 



'n th equation, y = 25 log x, 

 to Jin<l 1/4 locvt. A table of logarithms 

 shows that this equation is satisfied by 

 the following pairs of values: 



0, y l = - co 



1. fi = 

 >, y. = 7.5 



8, = 11.0 



a , y f = 19.4 

 = 7, jr. 



=10. y, 

 = 15, y|t 

 20, y u =^ 



t. 



The corresponding points are : 

 ^5(0, -00), />, = (!, 0), />,=(!> 

 etc. ; and the locus of the above eqna- 

 tion is approximately given by the 



curve drawn through these points as shown in Fig. 1& 



