B6 



ANALYTIC QEOM1 ://;> 



6. A line hut the slope 6; what is its y-iiil- t passes through 

 the point (7. 1 



7. What must be the slope of a line whose y-intercept is 3, in order 

 that it may pass through the point (~5, 



8. Is the point (1, |) on the line passing through the point ( i>, -14), 

 and making an angle tan~' V with the z-axis? 



9. How <lo the lines y = 3z - 1, y = 3z + 7, and 2y - 6z -f 15 = 

 differ from each other? What have they in common? Draw these lines. 



10. What is common to the lines y = 3z-l, 2y = 5z-2, ami 

 7z -3y = 3? 



11. What is the slope of line [9] ? of line [10]? 



12. Derive equation [12] independently of equation [11]. 



54. Equation of straight line in terms of the perpendicular 

 from the origin upon it, and the angle which that perpendicular 

 makes with the x-axis. Let HK be the line whose equation 



is sought, and let the perpendicular (02V=;>) from upon 

 this line, and the angle (a) which this perpendicular m 

 with the ar-axis, be given. Also let P= (z, y) be any point 

 on HK\ then by projection upon &ZV(Art. 17), 



MPx\na= <>.Y. 



i/sina = ;>, . . . [13] 

 which is the required equation. 



Initiation [13] is known as the normal form of the equa- 

 tion of the straight line. 



In the following pages/? will always be regarded as posi- 

 .ind a as positive and less than 300. 





