'.; ANALYTIC GEOXETl;} [Cii. V. 



EXERCISES 



l i;<iiK-<> tho following equations to the intercept (symmetric) 

 form, and draw the lim-s which they represent 



(a) 3x-2y+12 = 0; 08) 3x - 2y + 1 = 5* + :J; 



(y) 2y = 15-y^ (8) ^pL-L = 0. 



2. Reduce to the slope form, and then trace the loci : 

 (a) y + 6(y-3*)=- 10z-r-4; (0) 3* + 2y + 6 =0; 



Whirl. i< the positive side of the line (ft) ? (cf. footnote, Art 



3. Reduce to the normal form, and then trace the loci : 

 (a) :Jx + 4y = 15; (ft) 3* - 4y + 15 = ; 



x-3y = 5 + 6x; (8) | x = y - 5. 



4. Show that the lines 3x + 5 = y and 6 x - 2y = 81 are parallel. 



5. What is the slope of the line between the two points (8, ~1) and 

 i '. What is its distance from the origin ' Which is its negative 



side? 



6. A line passes through the point (5, 6) and has its intercepts on 

 the axes equal and both positive. Find its equation and its distance 

 from the 



7. A straight line passes through the point (1, ~2) and is such that 

 the portion of it between the axes is bisected by that point. What is the 

 slope of the line ? 



8. What are the intercepts which the line through the points ( !.:') 

 and (6, 7) makes on the axes? -Through the points (a, 2 a) and (b, 



9. What system of lines obtained by varying the parameter b is rep- 

 resented by the equation y = 6 x + b ? 



10. What system of lines obtained by varying the parameter in is 

 represented by the equation y mx + 6? 



11. What family (system) of lines obtained by varying the param* t. r 

 a is represented by the equation x cos a -I- y sin a = 5? To what curve is 

 -:n -h line of the family tangent? 



12. Find cos a and sin a for the lines 



(a) y^mx + t, (ft) ;; + = >- 



(y) \ = , () 7i-5y+l=0. 



