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EXERCISES 

 .instruct the lines : 

 (a) ,cos<*-30-).ln; (r) p cos (* - j) ,0; 



,>-.m0 p cost* -). 



2. Find the polar equation* of straight linen at a distance 3 from the 

 pole, and: (1) parallel to the initial line; (>) perpendicular to the .. 

 line. 



* A straight line panes through the poiuU(5, -45) and (2, OO ); 

 find iu polar equal i 



4 Fiiul the polar equation of a line passing through a given point 

 (p,.0,)tti ut a given angle ^ = tan 



5. Find the polar coordinates of the point of intersection of the lines 



EXAMPLES ON CHAPTER V 



1. The point* (~1. . are the extr.-i.nurs of the base of 



an equilateral triangle. Find the equa ue sides, and the c 



nates of the third vertex. Two solutions. 



2 Thr i the rerticesof a parallelogram are at the points (1. 1). 



.and (5. '_). Find the fourth vertex. (Three solutions.) ! 

 also the area of the parallelogram. 



: .- 1 the equations of the two lines drawn through the point (0. 3). 

 that the perpendiculars let fall from the point (6, 6) upon them are 

 each of length 



4 I. ! ; ,~ i 1 .iiars are let fall from the point (5, 0) upon the sides of 

 the triangle whose vertices are at the points (4. > -5). 



Show that the feet of these three perpendiculars lie on a straight line. 



! the equa straight line 



5. tln-iuli the origin and the point of intersection of the lint- 

 * - y = 4 and 7x + y + 20 = 0. Prove that it is a bisector of the angle 

 formed by the two given lines. 



6. through the intersection of th- lit..-* 3x-4y + l=0 and 

 5x + y = 1. and cutting off equal intercepts from the axes. 



7. tl.n.u-h th.< i- and intersecting the line x + y = 4 at a 



VO from thi> |*iut. 



